5x^2+x=120

Solution for 5x^2+x=120 equation:

5x^2+x=120

We move all terms to the left:

5x^2+x-(120)=0

a = 5; b = 1; c = -120;
Δ = b2-4ac
Δ = 12-4·5·(-120)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-49}{2*5}=\frac{-50}{10}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+49}{2*5}=\frac{48}{10}
=4+4/5
$