81x^2-18=-7

Solution for 81x^2-18=-7 equation:

81x^2-18=-7

We move all terms to the left:

81x^2-18-(-7)=0

We add all the numbers together, and all the variables

81x^2-11=0

a = 81; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·81·(-11)
Δ = 3564
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:

$\sqrt{\Delta}=\sqrt{3564}=\sqrt{324*11}=\sqrt{324}*\sqrt{11}=18\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{11}}{2*81}=\frac{0-18\sqrt{11}}{162}
=-\frac{18\sqrt{11}}{162}
=-\frac{\sqrt{11}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{11}}{2*81}=\frac{0+18\sqrt{11}}{162}
=\frac{18\sqrt{11}}{162}
=\frac{\sqrt{11}}{9}
$