X^2-22x-140=0

Solution for X^2-22x-140=0 equation:

X^2-22X-140=0

a = 1; b = -22; c = -140;
Δ = b2-4ac
Δ = -222-4·1·(-140)
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-6\sqrt{29}}{2*1}=\frac{22-6\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+6\sqrt{29}}{2*1}=\frac{22+6\sqrt{29}}{2}
$