x2-24x=140

Solution for x2-24x=140 equation:

x2-24x=140

We move all terms to the left:

x2-24x-(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 = 1136
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:

$\sqrt{\Delta}=\sqrt{1136}=\sqrt{16*71}=\sqrt{16}*\sqrt{71}=4\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{71}}{2*1}=\frac{24-4\sqrt{71}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{71}}{2*1}=\frac{24+4\sqrt{71}}{2}
$