X^2-150x+1200=0

Solution for X^2-150x+1200=0 equation:

X^2-150X+1200=0

a = 1; b = -150; c = +1200;
Δ = b2-4ac
Δ = -1502-4·1·1200
Δ = 17700
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:

$\sqrt{\Delta}=\sqrt{17700}=\sqrt{100*177}=\sqrt{100}*\sqrt{177}=10\sqrt{177}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-10\sqrt{177}}{2*1}=\frac{150-10\sqrt{177}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+10\sqrt{177}}{2*1}=\frac{150+10\sqrt{177}}{2}
$