(4x^2)+(18x)-11=191

Solution for (4x^2)+(18x)-11=191 equation:

(4x^2)+(18x)-11=191

We move all terms to the left:

(4x^2)+(18x)-11-(191)=0

We add all the numbers together, and all the variables

4x^2+18x-202=0

a = 4; b = 18; c = -202;
Δ = b2-4ac
Δ = 182-4·4·(-202)
Δ = 3556
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:

$\sqrt{\Delta}=\sqrt{3556}=\sqrt{4*889}=\sqrt{4}*\sqrt{889}=2\sqrt{889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{889}}{2*4}=\frac{-18-2\sqrt{889}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{889}}{2*4}=\frac{-18+2\sqrt{889}}{8}
$