2x+(5x-3)=x(-4x+1)-5x

Solution for 2x+(5x-3)=x(-4x+1)-5x equation:

2x+(5x-3)=x(-4x+1)-5x

We move all terms to the left:

2x+(5x-3)-(x(-4x+1)-5x)=0

We get rid of parentheses

2x+5x-(x(-4x+1)-5x)-3=0


We calculate terms in parentheses: -(x(-4x+1)-5x), so:

x(-4x+1)-5x

We add all the numbers together, and all the variables

-5x+x(-4x+1)

We multiply parentheses

-4x^2-5x+x

We add all the numbers together, and all the variables

-4x^2-4x

Back to the equation:

-(-4x^2-4x)


We add all the numbers together, and all the variables

-(-4x^2-4x)+7x-3=0

We get rid of parentheses

4x^2+4x+7x-3=0

We add all the numbers together, and all the variables

4x^2+11x-3=0

a = 4; b = 11; c = -3;
Δ = b2-4ac
Δ = 112-4·4·(-3)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-13}{2*4}=\frac{-24}{8}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+13}{2*4}=\frac{2}{8}
=1/4
$