8(x2=6)-5=171

Solution for 8(x2=6)-5=171 equation:

8(x2=6)-5=171

We move all terms to the left:

8(x2-(6)-5)=0

We add all the numbers together, and all the variables

8(+x^2-6-5)=0

We multiply parentheses

8x^2-48-40=0

We add all the numbers together, and all the variables

8x^2-88=0

a = 8; b = 0; c = -88;
Δ = b2-4ac
Δ = 02-4·8·(-88)
Δ = 2816
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:

$\sqrt{\Delta}=\sqrt{2816}=\sqrt{256*11}=\sqrt{256}*\sqrt{11}=16\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{11}}{2*8}=\frac{0-16\sqrt{11}}{16}
=-\frac{16\sqrt{11}}{16}
=-\sqrt{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{11}}{2*8}=\frac{0+16\sqrt{11}}{16}
=\frac{16\sqrt{11}}{16}
=\sqrt{11}
$