x(x-8)+(x-2)(x-3)=175

Solution for x(x-8)+(x-2)(x-3)=175 equation:

x(x-8)+(x-2)(x-3)=175

We move all terms to the left:

x(x-8)+(x-2)(x-3)-(175)=0

We multiply parentheses

x^2-8x+(x-2)(x-3)-175=0

We multiply parentheses ..

x^2+(+x^2-3x-2x+6)-8x-175=0

We get rid of parentheses

x^2+x^2-3x-2x-8x+6-175=0

We add all the numbers together, and all the variables

2x^2-13x-169=0

a = 2; b = -13; c = -169;
Δ = b2-4ac
Δ = -132-4·2·(-169)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-39}{2*2}=\frac{-26}{4}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+39}{2*2}=\frac{52}{4}
=13
$