x^2+150x=8400

Solution for x^2+150x=8400 equation:

x^2+150x=8400

We move all terms to the left:

x^2+150x-(8400)=0

a = 1; b = 150; c = -8400;
Δ = b2-4ac
Δ = 1502-4·1·(-8400)
Δ = 56100
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:

$\sqrt{\Delta}=\sqrt{56100}=\sqrt{100*561}=\sqrt{100}*\sqrt{561}=10\sqrt{561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-10\sqrt{561}}{2*1}=\frac{-150-10\sqrt{561}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+10\sqrt{561}}{2*1}=\frac{-150+10\sqrt{561}}{2}
$