10E32=(10E8+x)(x)

Solution for 10E32=(10E8+x)(x) equation:

1032=(108+E)(E)

We move all terms to the left:

1032-((108+E)(E))=0

We add all the numbers together, and all the variables

-((E+108)E)+1032=0


We calculate terms in parentheses: -((E+108)E), so:

(E+108)E

We multiply parentheses

E^2+108E

Back to the equation:

-(E^2+108E)


We get rid of parentheses

-E^2-108E+1032=0

We add all the numbers together, and all the variables

-1E^2-108E+1032=0

a = -1; b = -108; c = +1032;
Δ = b2-4ac
Δ = -1082-4·(-1)·1032
Δ = 15792
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{15792}=\sqrt{16*987}=\sqrt{16}*\sqrt{987}=4\sqrt{987}$
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-4\sqrt{987}}{2*-1}=\frac{108-4\sqrt{987}}{-2}
$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+4\sqrt{987}}{2*-1}=\frac{108+4\sqrt{987}}{-2}
$