17y^2+12y=25^2

Solution for 17y^2+12y=25^2 equation:

17y^2+12y=25^2

We move all terms to the left:

17y^2+12y-(25^2)=0

We add all the numbers together, and all the variables

17y^2+12y-625=0

a = 17; b = 12; c = -625;
Δ = b2-4ac
Δ = 122-4·17·(-625)
Δ = 42644
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{42644}=\sqrt{4*10661}=\sqrt{4}*\sqrt{10661}=2\sqrt{10661}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{10661}}{2*17}=\frac{-12-2\sqrt{10661}}{34}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{10661}}{2*17}=\frac{-12+2\sqrt{10661}}{34}
$