X^2-24x=-70

Solution for X^2-24x=-70 equation:

X^2-24X=-70

We move all terms to the left:

X^2-24X-(-70)=0

We add all the numbers together, and all the variables

X^2-24X+70=0

a = 1; b = -24; c = +70;
Δ = b2-4ac
Δ = -242-4·1·70
Δ = 296
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:

$\sqrt{\Delta}=\sqrt{296}=\sqrt{4*74}=\sqrt{4}*\sqrt{74}=2\sqrt{74}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{74}}{2*1}=\frac{24-2\sqrt{74}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{74}}{2*1}=\frac{24+2\sqrt{74}}{2}
$