(x+2)(x-3)=175

Solution for (x+2)(x-3)=175 equation:

(X+2)(X-3)=175

We move all terms to the left:

(X+2)(X-3)-(175)=0

We multiply parentheses ..

(+X^2-3X+2X-6)-175=0

We get rid of parentheses

X^2-3X+2X-6-175=0

We add all the numbers together, and all the variables

X^2-1X-181=0

a = 1; b = -1; c = -181;
Δ = b2-4ac
Δ = -12-4·1·(-181)
Δ = 725
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{725}=\sqrt{25*29}=\sqrt{25}*\sqrt{29}=5\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5\sqrt{29}}{2*1}=\frac{1-5\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5\sqrt{29}}{2*1}=\frac{1+5\sqrt{29}}{2}
$