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

Solution for 5x^2=10x^2-(5-x) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(10x^2-(-1x+5)), so:

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

We get rid of parentheses

10x^2+1x-5

We add all the numbers together, and all the variables

10x^2+x-5

Back to the equation:

-(10x^2+x-5)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-5x^2-1x+5=0

a = -5; b = -1; c = +5;
Δ = b2-4ac
Δ = -12-4·(-5)·5
Δ = 101
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{101}}{2*-5}=\frac{1-\sqrt{101}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{101}}{2*-5}=\frac{1+\sqrt{101}}{-10}
$