-7-4x^2=-239

Solution for -7-4x^2=-239 equation:

-7-4x^2=-239

We move all terms to the left:

-7-4x^2-(-239)=0

We add all the numbers together, and all the variables

-4x^2+232=0

a = -4; b = 0; c = +232;
Δ = b2-4ac
Δ = 02-4·(-4)·232
Δ = 3712
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:

$\sqrt{\Delta}=\sqrt{3712}=\sqrt{64*58}=\sqrt{64}*\sqrt{58}=8\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{58}}{2*-4}=\frac{0-8\sqrt{58}}{-8}
=-\frac{8\sqrt{58}}{-8}
=-\frac{\sqrt{58}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{58}}{2*-4}=\frac{0+8\sqrt{58}}{-8}
=\frac{8\sqrt{58}}{-8}
=\frac{\sqrt{58}}{-1}
$