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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((5x-4)2x), so:

(5x-4)2x

We multiply parentheses

10x^2-8x

Back to the equation:

-(10x^2-8x)


We get rid of parentheses

3x^2-10x^2+3x+2x+8x+2=0

We add all the numbers together, and all the variables

-7x^2+13x+2=0

a = -7; b = 13; c = +2;
Δ = b2-4ac
Δ = 132-4·(-7)·2
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-15}{2*-7}=\frac{-28}{-14}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+15}{2*-7}=\frac{2}{-14}
=-1/7
$