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

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

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

We move all terms to the left:

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

We get rid of parentheses

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


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

x(2x+3)

We multiply parentheses

2x^2+3x

Back to the equation:

-(2x^2+3x)


We add all the numbers together, and all the variables

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

We get rid of parentheses

-2x^2-2x-3x+1=0

We add all the numbers together, and all the variables

-2x^2-5x+1=0

a = -2; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·(-2)·1
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{33}}{2*-2}=\frac{5-\sqrt{33}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{33}}{2*-2}=\frac{5+\sqrt{33}}{-4}
$