x(x-7)-5(x-2)=2

Solution for x(x-7)-5(x-2)=2 equation:

x(x-7)-5(x-2)=2

We move all terms to the left:

x(x-7)-5(x-2)-(2)=0

We multiply parentheses

x^2-7x-5x+10-2=0

We add all the numbers together, and all the variables

x^2-12x+8=0

a = 1; b = -12; c = +8;
Δ = b2-4ac
Δ = -122-4·1·8
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{7}}{2*1}=\frac{12-4\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{7}}{2*1}=\frac{12+4\sqrt{7}}{2}
$