x^2-7x=150

Solution for x^2-7x=150 equation:

x^2-7x=150

We move all terms to the left:

x^2-7x-(150)=0

a = 1; b = -7; c = -150;
Δ = b2-4ac
Δ = -72-4·1·(-150)
Δ = 649
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{-(-7)-\sqrt{649}}{2*1}=\frac{7-\sqrt{649}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{649}}{2*1}=\frac{7+\sqrt{649}}{2}
$