(y+4)(y-7)=18

Solution for (y+4)(y-7)=18 equation:

(y+4)(y-7)=18

We move all terms to the left:

(y+4)(y-7)-(18)=0

We multiply parentheses ..

(+y^2-7y+4y-28)-18=0

We get rid of parentheses

y^2-7y+4y-28-18=0

We add all the numbers together, and all the variables

y^2-3y-46=0

a = 1; b = -3; c = -46;
Δ = b2-4ac
Δ = -32-4·1·(-46)
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{193}}{2*1}=\frac{3-\sqrt{193}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{193}}{2*1}=\frac{3+\sqrt{193}}{2}
$