168x^2-27=85

Solution for 168x^2-27=85 equation:

168x^2-27=85

We move all terms to the left:

168x^2-27-(85)=0

We add all the numbers together, and all the variables

168x^2-112=0

a = 168; b = 0; c = -112;
Δ = b2-4ac
Δ = 02-4·168·(-112)
Δ = 75264
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:

$\sqrt{\Delta}=\sqrt{75264}=\sqrt{12544*6}=\sqrt{12544}*\sqrt{6}=112\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-112\sqrt{6}}{2*168}=\frac{0-112\sqrt{6}}{336}
=-\frac{112\sqrt{6}}{336}
=-\frac{\sqrt{6}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+112\sqrt{6}}{2*168}=\frac{0+112\sqrt{6}}{336}
=\frac{112\sqrt{6}}{336}
=\frac{\sqrt{6}}{3}
$