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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(x+2)-(5(2x-5)x)+3=0

We get rid of parentheses

-x-(5(2x-5)x)-2+3=0


We calculate terms in parentheses: -(5(2x-5)x), so:

5(2x-5)x

We multiply parentheses

10x^2-25x

Back to the equation:

-(10x^2-25x)


We add all the numbers together, and all the variables

-1x-(10x^2-25x)+1=0

We get rid of parentheses

-10x^2-1x+25x+1=0

We add all the numbers together, and all the variables

-10x^2+24x+1=0

a = -10; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·(-10)·1
Δ = 616
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:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{154}}{2*-10}=\frac{-24-2\sqrt{154}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{154}}{2*-10}=\frac{-24+2\sqrt{154}}{-20}
$