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

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

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

We move all terms to the left:

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

We multiply parentheses

10x-((3x+1)(x-3))-5=0

We multiply parentheses ..

-((+3x^2-9x+x-3))+10x-5=0


We calculate terms in parentheses: -((+3x^2-9x+x-3)), so:

(+3x^2-9x+x-3)

We get rid of parentheses

3x^2-9x+x-3

We add all the numbers together, and all the variables

3x^2-8x-3

Back to the equation:

-(3x^2-8x-3)


We add all the numbers together, and all the variables

10x-(3x^2-8x-3)-5=0

We get rid of parentheses

-3x^2+10x+8x+3-5=0

We add all the numbers together, and all the variables

-3x^2+18x-2=0

a = -3; b = 18; c = -2;
Δ = b2-4ac
Δ = 182-4·(-3)·(-2)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-10\sqrt{3}}{2*-3}=\frac{-18-10\sqrt{3}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+10\sqrt{3}}{2*-3}=\frac{-18+10\sqrt{3}}{-6}
$