x^2-89=7x

Solution for x^2-89=7x equation:

x^2-89=7x

We move all terms to the left:

x^2-89-(7x)=0

a = 1; b = -7; c = -89;
Δ = b2-4ac
Δ = -72-4·1·(-89)
Δ = 405
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:

$\sqrt{\Delta}=\sqrt{405}=\sqrt{81*5}=\sqrt{81}*\sqrt{5}=9\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-9\sqrt{5}}{2*1}=\frac{7-9\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+9\sqrt{5}}{2*1}=\frac{7+9\sqrt{5}}{2}
$