(1/2y+14)(y-8)=180

Solution for (1/2y+14)(y-8)=180 equation:

(1/2y+14)(y-8)=180

We move all terms to the left:

(1/2y+14)(y-8)-(180)=0


Domain of the equation: 2y+14)(y-8)!=0

y∈R


We multiply parentheses ..

(+y^2-8y+14y-112)-180=0

We get rid of parentheses

y^2-8y+14y-112-180=0

We add all the numbers together, and all the variables

y^2+6y-292=0

a = 1; b = 6; c = -292;
Δ = b2-4ac
Δ = 62-4·1·(-292)
Δ = 1204
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:

$\sqrt{\Delta}=\sqrt{1204}=\sqrt{4*301}=\sqrt{4}*\sqrt{301}=2\sqrt{301}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{301}}{2*1}=\frac{-6-2\sqrt{301}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{301}}{2*1}=\frac{-6+2\sqrt{301}}{2}
$