191-4x2=-20

Solution for 191-4x2=-20 equation:

191-4x^2=-20

We move all terms to the left:

191-4x^2-(-20)=0

We add all the numbers together, and all the variables

-4x^2+211=0

a = -4; b = 0; c = +211;
Δ = b2-4ac
Δ = 02-4·(-4)·211
Δ = 3376
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:

$\sqrt{\Delta}=\sqrt{3376}=\sqrt{16*211}=\sqrt{16}*\sqrt{211}=4\sqrt{211}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{211}}{2*-4}=\frac{0-4\sqrt{211}}{-8}
=-\frac{4\sqrt{211}}{-8}
=-\frac{\sqrt{211}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{211}}{2*-4}=\frac{0+4\sqrt{211}}{-8}
=\frac{4\sqrt{211}}{-8}
=\frac{\sqrt{211}}{-2}
$