x^2+1x=5x^2-10x

Solution for x^2+1x=5x^2-10x equation:

x^2+1x=5x^2-10x

We move all terms to the left:

x^2+1x-(5x^2-10x)=0

We add all the numbers together, and all the variables

x^2+x-(5x^2-10x)=0

We get rid of parentheses

x^2-5x^2+x+10x=0

We add all the numbers together, and all the variables

-4x^2+11x=0

a = -4; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-4)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-4}=\frac{-22}{-8}
=2+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-4}=\frac{0}{-8}
=0
$