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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-3x+5x-(2x(x+5))+10=0


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

2x(x+5)

We multiply parentheses

2x^2+10x

Back to the equation:

-(2x^2+10x)


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2-8x+10=0

a = -2; b = -8; c = +10;
Δ = b2-4ac
Δ = -82-4·(-2)·10
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12}{2*-2}=\frac{-4}{-4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12}{2*-2}=\frac{20}{-4}
=-5
$