7x^2-50x=120

Solution for 7x^2-50x=120 equation:

7x^2-50x=120

We move all terms to the left:

7x^2-50x-(120)=0

a = 7; b = -50; c = -120;
Δ = b2-4ac
Δ = -502-4·7·(-120)
Δ = 5860
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:

$\sqrt{\Delta}=\sqrt{5860}=\sqrt{4*1465}=\sqrt{4}*\sqrt{1465}=2\sqrt{1465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{1465}}{2*7}=\frac{50-2\sqrt{1465}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{1465}}{2*7}=\frac{50+2\sqrt{1465}}{14}
$