34=x2-4(7+82)

Solution for 34=x2-4(7+82) equation:

34=x2-4(7+82)

We move all terms to the left:

34-(x2-4(7+82))=0

We add all the numbers together, and all the variables

-(x2-489)+34=0

We get rid of parentheses

-x2+489+34=0

We add all the numbers together, and all the variables

-1x^2+523=0

a = -1; b = 0; c = +523;
Δ = b2-4ac
Δ = 02-4·(-1)·523
Δ = 2092
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:

$\sqrt{\Delta}=\sqrt{2092}=\sqrt{4*523}=\sqrt{4}*\sqrt{523}=2\sqrt{523}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{523}}{2*-1}=\frac{0-2\sqrt{523}}{-2}
=-\frac{2\sqrt{523}}{-2}
=-\frac{\sqrt{523}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{523}}{2*-1}=\frac{0+2\sqrt{523}}{-2}
=\frac{2\sqrt{523}}{-2}
=\frac{\sqrt{523}}{-1}
$