x2-142x=24

Solution for x2-142x=24 equation:

x2-142x=24

We move all terms to the left:

x2-142x-(24)=0

We add all the numbers together, and all the variables

x^2-142x-24=0

a = 1; b = -142; c = -24;
Δ = b2-4ac
Δ = -1422-4·1·(-24)
Δ = 20260
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:

$\sqrt{\Delta}=\sqrt{20260}=\sqrt{4*5065}=\sqrt{4}*\sqrt{5065}=2\sqrt{5065}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-142)-2\sqrt{5065}}{2*1}=\frac{142-2\sqrt{5065}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-142)+2\sqrt{5065}}{2*1}=\frac{142+2\sqrt{5065}}{2}
$