4y(y-12)=26

Solution for 4y(y-12)=26 equation:

4y(y-12)=26

We move all terms to the left:

4y(y-12)-(26)=0

We multiply parentheses

4y^2-48y-26=0

a = 4; b = -48; c = -26;
Δ = b2-4ac
Δ = -482-4·4·(-26)
Δ = 2720
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:

$\sqrt{\Delta}=\sqrt{2720}=\sqrt{16*170}=\sqrt{16}*\sqrt{170}=4\sqrt{170}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{170}}{2*4}=\frac{48-4\sqrt{170}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{170}}{2*4}=\frac{48+4\sqrt{170}}{8}
$