10x*5x=90

Solution for 10x*5x=90 equation:

10x*5x=90

We move all terms to the left:

10x*5x-(90)=0

Wy multiply elements

50x^2-90=0

a = 50; b = 0; c = -90;
Δ = b2-4ac
Δ = 02-4·50·(-90)
Δ = 18000
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:

$\sqrt{\Delta}=\sqrt{18000}=\sqrt{3600*5}=\sqrt{3600}*\sqrt{5}=60\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{5}}{2*50}=\frac{0-60\sqrt{5}}{100}
=-\frac{60\sqrt{5}}{100}
=-\frac{3\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{5}}{2*50}=\frac{0+60\sqrt{5}}{100}
=\frac{60\sqrt{5}}{100}
=\frac{3\sqrt{5}}{5}
$