X+10x^2-12x=x^2+2x

Solution for X+10x^2-12x=x^2+2x equation:

X+10X^2-12X=X^2+2X

We move all terms to the left:

X+10X^2-12X-(X^2+2X)=0

We add all the numbers together, and all the variables

10X^2-11X-(X^2+2X)=0

We get rid of parentheses

10X^2-X^2-11X-2X=0

We add all the numbers together, and all the variables

9X^2-13X=0

a = 9; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·9·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*9}=\frac{0}{18}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*9}=\frac{26}{18}
=1+4/9
$