25x*x+90000=100x*x

Solution for 25x*x+90000=100x*x equation:

25x*x+90000=100x*x

We move all terms to the left:

25x*x+90000-(100x*x)=0

We add all the numbers together, and all the variables

25x*x-(+100x*x)+90000=0

Wy multiply elements

25x^2-(+100x*x)+90000=0

We get rid of parentheses

25x^2-100x*x+90000=0

Wy multiply elements

25x^2-100x^2+90000=0

We add all the numbers together, and all the variables

-75x^2+90000=0

a = -75; b = 0; c = +90000;
Δ = b2-4ac
Δ = 02-4·(-75)·90000
Δ = 27000000
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:

$\sqrt{\Delta}=\sqrt{27000000}=\sqrt{9000000*3}=\sqrt{9000000}*\sqrt{3}=3000\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3000\sqrt{3}}{2*-75}=\frac{0-3000\sqrt{3}}{-150}
=-\frac{3000\sqrt{3}}{-150}
=-\frac{20\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3000\sqrt{3}}{2*-75}=\frac{0+3000\sqrt{3}}{-150}
=\frac{3000\sqrt{3}}{-150}
=\frac{20\sqrt{3}}{-1}
$