0=4x^2-47x+120

Solution for 0=4x^2-47x+120 equation:

0=4x^2-47x+120

We move all terms to the left:

0-(4x^2-47x+120)=0

We add all the numbers together, and all the variables

-(4x^2-47x+120)=0

We get rid of parentheses

-4x^2+47x-120=0

a = -4; b = 47; c = -120;
Δ = b2-4ac
Δ = 472-4·(-4)·(-120)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-17}{2*-4}=\frac{-64}{-8}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+17}{2*-4}=\frac{-30}{-8}
=3+3/4
$