(x-6)(x+3)/2=22

Solution for (x-6)(x+3)/2=22 equation:

(x-6)(x+3)/2=22

We move all terms to the left:

(x-6)(x+3)/2-(22)=0

We multiply parentheses ..

(+x^2+3x-6x-18)/2-22=0

We multiply all the terms by the denominator


(+x^2+3x-6x-18)-22*2=0

We add all the numbers together, and all the variables

(+x^2+3x-6x-18)-44=0

We get rid of parentheses

x^2+3x-6x-18-44=0

We add all the numbers together, and all the variables

x^2-3x-62=0

a = 1; b = -3; c = -62;
Δ = b2-4ac
Δ = -32-4·1·(-62)
Δ = 257
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{257}}{2*1}=\frac{3-\sqrt{257}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{257}}{2*1}=\frac{3+\sqrt{257}}{2}
$