190=x^2+4x-12

Solution for 190=x^2+4x-12 equation:

190=x^2+4x-12

We move all terms to the left:

190-(x^2+4x-12)=0

We get rid of parentheses

-x^2-4x+12+190=0

We add all the numbers together, and all the variables

-1x^2-4x+202=0

a = -1; b = -4; c = +202;
Δ = b2-4ac
Δ = -42-4·(-1)·202
Δ = 824
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:

$\sqrt{\Delta}=\sqrt{824}=\sqrt{4*206}=\sqrt{4}*\sqrt{206}=2\sqrt{206}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{206}}{2*-1}=\frac{4-2\sqrt{206}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{206}}{2*-1}=\frac{4+2\sqrt{206}}{-2}
$