x=-2x^2+188

Solution for x=-2x^2+188 equation:

x=-2x^2+188

We move all terms to the left:

x-(-2x^2+188)=0

We get rid of parentheses

2x^2+x-188=0

a = 2; b = 1; c = -188;
Δ = b2-4ac
Δ = 12-4·2·(-188)
Δ = 1505
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{-(1)-\sqrt{1505}}{2*2}=\frac{-1-\sqrt{1505}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1505}}{2*2}=\frac{-1+\sqrt{1505}}{4}
$