x^2-12x=35=0

Solution for x^2-12x=35=0 equation:

x^2-12x=35=0

We move all terms to the left:

x^2-12x-(35)=0

a = 1; b = -12; c = -35;
Δ = b2-4ac
Δ = -122-4·1·(-35)
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{71}}{2*1}=\frac{12-2\sqrt{71}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{71}}{2*1}=\frac{12+2\sqrt{71}}{2}
$