(5x-2)(x+1)=x(4-10x)

Solution for (5x-2)(x+1)=x(4-10x) equation:

(5x-2)(x+1)=x(4-10x)

We move all terms to the left:

(5x-2)(x+1)-(x(4-10x))=0

We add all the numbers together, and all the variables

(5x-2)(x+1)-(x(-10x+4))=0

We multiply parentheses ..

(+5x^2+5x-2x-2)-(x(-10x+4))=0


We calculate terms in parentheses: -(x(-10x+4)), so:

x(-10x+4)

We multiply parentheses

-10x^2+4x

Back to the equation:

-(-10x^2+4x)


We get rid of parentheses

5x^2+10x^2+5x-2x-4x-2=0

We add all the numbers together, and all the variables

15x^2-1x-2=0

a = 15; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·15·(-2)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*15}=\frac{-10}{30}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*15}=\frac{12}{30}
=2/5
$