x(x+5)=x-(4x-2)

Solution for x(x+5)=x-(4x-2) equation:

x(x+5)=x-(4x-2)

We move all terms to the left:

x(x+5)-(x-(4x-2))=0

We multiply parentheses

x^2+5x-(x-(4x-2))=0


We calculate terms in parentheses: -(x-(4x-2)), so:

x-(4x-2)

We get rid of parentheses

x-4x+2

We add all the numbers together, and all the variables

-3x+2

Back to the equation:

-(-3x+2)


We get rid of parentheses

x^2+5x+3x-2=0

We add all the numbers together, and all the variables

x^2+8x-2=0

a = 1; b = 8; c = -2;
Δ = b2-4ac
Δ = 82-4·1·(-2)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6\sqrt{2}}{2*1}=\frac{-8-6\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6\sqrt{2}}{2*1}=\frac{-8+6\sqrt{2}}{2}
$