2y^2=5y+12y=

Solution for 2y^2=5y+12y= equation:

2y^2=5y+12y=

We move all terms to the left:

2y^2-(5y+12y)=0

We add all the numbers together, and all the variables

2y^2-(+17y)=0

We get rid of parentheses

2y^2-17y=0

a = 2; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·2·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*2}=\frac{0}{4}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*2}=\frac{34}{4}
=8+1/2
$