(4x^2)+(18x)-11=180

Solution for (4x^2)+(18x)-11=180 equation:

(4x^2)+(18x)-11=180

We move all terms to the left:

(4x^2)+(18x)-11-(180)=0

We add all the numbers together, and all the variables

4x^2+18x-191=0

a = 4; b = 18; c = -191;
Δ = b2-4ac
Δ = 182-4·4·(-191)
Δ = 3380
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3380}=\sqrt{676*5}=\sqrt{676}*\sqrt{5}=26\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-26\sqrt{5}}{2*4}=\frac{-18-26\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+26\sqrt{5}}{2*4}=\frac{-18+26\sqrt{5}}{8}
$