0=4x^2-40x+91

Solution for 0=4x^2-40x+91 equation:

0=4x^2-40x+91

We move all terms to the left:

0-(4x^2-40x+91)=0

We add all the numbers together, and all the variables

-(4x^2-40x+91)=0

We get rid of parentheses

-4x^2+40x-91=0

a = -4; b = 40; c = -91;
Δ = b2-4ac
Δ = 402-4·(-4)·(-91)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-12}{2*-4}=\frac{-52}{-8}
=6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+12}{2*-4}=\frac{-28}{-8}
=3+1/2
$