0=20x^2-31x-142

Solution for 0=20x^2-31x-142 equation:

0=20x^2-31x-142

We move all terms to the left:

0-(20x^2-31x-142)=0

We add all the numbers together, and all the variables

-(20x^2-31x-142)=0

We get rid of parentheses

-20x^2+31x+142=0

a = -20; b = 31; c = +142;
Δ = b2-4ac
Δ = 312-4·(-20)·142
Δ = 12321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12321}=111$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-111}{2*-20}=\frac{-142}{-40}
=3+11/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+111}{2*-20}=\frac{80}{-40}
=-2
$