x^2-3x=150

Solution for x^2-3x=150 equation:

x^2-3x=150

We move all terms to the left:

x^2-3x-(150)=0

a = 1; b = -3; c = -150;
Δ = b2-4ac
Δ = -32-4·1·(-150)
Δ = 609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{609}}{2*1}=\frac{3-\sqrt{609}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{609}}{2*1}=\frac{3+\sqrt{609}}{2}
$