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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

(+3x^2-3x+2x-2)

We get rid of parentheses

3x^2-3x+2x-2

We add all the numbers together, and all the variables

3x^2-1x-2

Back to the equation:

-(3x^2-1x-2)


We add all the numbers together, and all the variables

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

We get rid of parentheses

-3x^2+5x+1x+2-3=0

We add all the numbers together, and all the variables

-3x^2+6x-1=0

a = -3; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·(-3)·(-1)
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{6}}{2*-3}=\frac{-6-2\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{6}}{2*-3}=\frac{-6+2\sqrt{6}}{-6}
$