85=(x^2-3)

Solution for 85=(x^2-3) equation:

85=(x^2-3)

We move all terms to the left:

85-((x^2-3))=0


We calculate terms in parentheses: -((x^2-3)), so:

(x^2-3)

We get rid of parentheses

x^2-3

Back to the equation:

-(x^2-3)


We get rid of parentheses

-x^2+3+85=0

We add all the numbers together, and all the variables

-1x^2+88=0

a = -1; b = 0; c = +88;
Δ = b2-4ac
Δ = 02-4·(-1)·88
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{22}}{2*-1}=\frac{0-4\sqrt{22}}{-2}
=-\frac{4\sqrt{22}}{-2}
=-\frac{2\sqrt{22}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{22}}{2*-1}=\frac{0+4\sqrt{22}}{-2}
=\frac{4\sqrt{22}}{-2}
=\frac{2\sqrt{22}}{-1}
$