x^2+(-12x)=17

Solution for x^2+(-12x)=17 equation:

x^2+(-12x)=17

We move all terms to the left:

x^2+(-12x)-(17)=0

We get rid of parentheses

x^2-12x-17=0

a = 1; b = -12; c = -17;
Δ = b2-4ac
Δ = -122-4·1·(-17)
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{53}}{2*1}=\frac{12-2\sqrt{53}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{53}}{2*1}=\frac{12+2\sqrt{53}}{2}
$