-5(x+2)=(-5X+1)X

Solution for -5(x+2)=(-5X+1)X equation:

-5(x+2)=(-5x+1)x

We move all terms to the left:

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

We multiply parentheses

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


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

(-5x+1)x

We multiply parentheses

-5x^2+x

Back to the equation:

-(-5x^2+x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

5x^2-6x-10=0

a = 5; b = -6; c = -10;
Δ = b2-4ac
Δ = -62-4·5·(-10)
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{59}}{2*5}=\frac{6-2\sqrt{59}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{59}}{2*5}=\frac{6+2\sqrt{59}}{10}
$