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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

2x^2+5x+6x-(3(2x-1))=0


We calculate terms in parentheses: -(3(2x-1)), so:

3(2x-1)

We multiply parentheses

6x-3

Back to the equation:

-(6x-3)


We add all the numbers together, and all the variables

2x^2+11x-(6x-3)=0

We get rid of parentheses

2x^2+11x-6x+3=0

We add all the numbers together, and all the variables

2x^2+5x+3=0

a = 2; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·2·3
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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