5x*10x=86

Solution for 5x*10x=86 equation:

5x*10x=86

We move all terms to the left:

5x*10x-(86)=0

Wy multiply elements

50x^2-86=0

a = 50; b = 0; c = -86;
Δ = b2-4ac
Δ = 02-4·50·(-86)
Δ = 17200
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:

$\sqrt{\Delta}=\sqrt{17200}=\sqrt{400*43}=\sqrt{400}*\sqrt{43}=20\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{43}}{2*50}=\frac{0-20\sqrt{43}}{100}
=-\frac{20\sqrt{43}}{100}
=-\frac{\sqrt{43}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{43}}{2*50}=\frac{0+20\sqrt{43}}{100}
=\frac{20\sqrt{43}}{100}
=\frac{\sqrt{43}}{5}
$