0=7x^2-247x+120

Solution for 0=7x^2-247x+120 equation:

0=7x^2-247x+120

We move all terms to the left:

0-(7x^2-247x+120)=0

We add all the numbers together, and all the variables

-(7x^2-247x+120)=0

We get rid of parentheses

-7x^2+247x-120=0

a = -7; b = 247; c = -120;
Δ = b2-4ac
Δ = 2472-4·(-7)·(-120)
Δ = 57649
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{-(247)-\sqrt{57649}}{2*-7}=\frac{-247-\sqrt{57649}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(247)+\sqrt{57649}}{2*-7}=\frac{-247+\sqrt{57649}}{-14}
$