x^2-24x=-140

Solution for x^2-24x=-140 equation:

x^2-24x=-140

We move all terms to the left:

x^2-24x-(-140)=0

We add all the numbers together, and all the variables

x^2-24x+140=0

a = 1; b = -24; c = +140;
Δ = b2-4ac
Δ = -242-4·1·140
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4}{2*1}=\frac{20}{2}
=10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4}{2*1}=\frac{28}{2}
=14
$