Question

Solve each equation by factoring or by using the quadratic formula. The quadratic formula is:

If $a{x}^2+bx+c=0$, with$a\ne 0$, then$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.

$15+4y^2=17y$

Short answer

The values of y are$y=3$and$y=\frac{5}{4}$.

Step-by-step solution

- Understand the concept used 

If$a{x}^2+bx+c=0$ , with$a\ne 0$, then$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . Solving using factoring can be done by splitting the middle term of equation and then making groups and equating them to zero.

- Substitute the values 

It is given that$15+4y^2=17y$which can also be written as$4y^2-17y+15=0$ .Using quadratic formula$y=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, substitute 4 for a, -17 for b and 15 for c.

Put the values in the formula and get$y=\frac{-\left(-17\right)\pm \sqrt{{\left(-17\right)}^2-4\times \left(4\right)\times \left(15\right)}}{2\left(4\right)}$ .

- Simplify for y 

Simplify the expression for y.