81x^2+100x^2=8100

Solution for 81x^2+100x^2=8100 equation:

81x^2+100x^2=8100

We move all terms to the left:

81x^2+100x^2-(8100)=0

We add all the numbers together, and all the variables

181x^2-8100=0

a = 181; b = 0; c = -8100;
Δ = b2-4ac
Δ = 02-4·181·(-8100)
Δ = 5864400
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:

$\sqrt{\Delta}=\sqrt{5864400}=\sqrt{32400*181}=\sqrt{32400}*\sqrt{181}=180\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-180\sqrt{181}}{2*181}=\frac{0-180\sqrt{181}}{362}
=-\frac{180\sqrt{181}}{362}
=-\frac{90\sqrt{181}}{181}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+180\sqrt{181}}{2*181}=\frac{0+180\sqrt{181}}{362}
=\frac{180\sqrt{181}}{362}
=\frac{90\sqrt{181}}{181}
$