y^2-6y=4y+156

Solution for y^2-6y=4y+156 equation:

y^2-6y=4y+156

We move all terms to the left:

y^2-6y-(4y+156)=0

We get rid of parentheses

y^2-6y-4y-156=0

We add all the numbers together, and all the variables

y^2-10y-156=0

a = 1; b = -10; c = -156;
Δ = b2-4ac
Δ = -102-4·1·(-156)
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{181}}{2*1}=\frac{10-2\sqrt{181}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{181}}{2*1}=\frac{10+2\sqrt{181}}{2}
$