81-4x2=10

Solution for 81-4x2=10 equation:

81-4x^2=10

We move all terms to the left:

81-4x^2-(10)=0

We add all the numbers together, and all the variables

-4x^2+71=0

a = -4; b = 0; c = +71;
Δ = b2-4ac
Δ = 02-4·(-4)·71
Δ = 1136
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:

$\sqrt{\Delta}=\sqrt{1136}=\sqrt{16*71}=\sqrt{16}*\sqrt{71}=4\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{71}}{2*-4}=\frac{0-4\sqrt{71}}{-8}
=-\frac{4\sqrt{71}}{-8}
=-\frac{\sqrt{71}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{71}}{2*-4}=\frac{0+4\sqrt{71}}{-8}
=\frac{4\sqrt{71}}{-8}
=\frac{\sqrt{71}}{-2}
$