X2+40x-150=0

Solution for X2+40x-150=0 equation:

X2+40X-150=0

We add all the numbers together, and all the variables

X^2+40X-150=0

a = 1; b = 40; c = -150;
Δ = b2-4ac
Δ = 402-4·1·(-150)
Δ = 2200
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:

$\sqrt{\Delta}=\sqrt{2200}=\sqrt{100*22}=\sqrt{100}*\sqrt{22}=10\sqrt{22}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-10\sqrt{22}}{2*1}=\frac{-40-10\sqrt{22}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+10\sqrt{22}}{2*1}=\frac{-40+10\sqrt{22}}{2}
$