0=4x^2-11x-55

Solution for 0=4x^2-11x-55 equation:

0=4x^2-11x-55

We move all terms to the left:

0-(4x^2-11x-55)=0

We add all the numbers together, and all the variables

-(4x^2-11x-55)=0

We get rid of parentheses

-4x^2+11x+55=0

a = -4; b = 11; c = +55;
Δ = b2-4ac
Δ = 112-4·(-4)·55
Δ = 1001
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{-(11)-\sqrt{1001}}{2*-4}=\frac{-11-\sqrt{1001}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{1001}}{2*-4}=\frac{-11+\sqrt{1001}}{-8}
$