x^2=10x^2-70x+100

Solution for x^2=10x^2-70x+100 equation:

x^2=10x^2-70x+100

We move all terms to the left:

x^2-(10x^2-70x+100)=0

We get rid of parentheses

x^2-10x^2+70x-100=0

We add all the numbers together, and all the variables

-9x^2+70x-100=0

a = -9; b = 70; c = -100;
Δ = b2-4ac
Δ = 702-4·(-9)·(-100)
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-10\sqrt{13}}{2*-9}=\frac{-70-10\sqrt{13}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+10\sqrt{13}}{2*-9}=\frac{-70+10\sqrt{13}}{-18}
$