7-9x^2=-76

Solution for 7-9x^2=-76 equation:

7-9x^2=-76

We move all terms to the left:

7-9x^2-(-76)=0

We add all the numbers together, and all the variables

-9x^2+83=0

a = -9; b = 0; c = +83;
Δ = b2-4ac
Δ = 02-4·(-9)·83
Δ = 2988
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:

$\sqrt{\Delta}=\sqrt{2988}=\sqrt{36*83}=\sqrt{36}*\sqrt{83}=6\sqrt{83}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{83}}{2*-9}=\frac{0-6\sqrt{83}}{-18}
=-\frac{6\sqrt{83}}{-18}
=-\frac{\sqrt{83}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{83}}{2*-9}=\frac{0+6\sqrt{83}}{-18}
=\frac{6\sqrt{83}}{-18}
=\frac{\sqrt{83}}{-3}
$