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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

x(x+1)

We multiply parentheses

x^2+x

Back to the equation:

-(x^2+x)


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = 5; c = +2;
Δ = b2-4ac
Δ = 52-4·(-1)·2
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*-1}=\frac{-5-\sqrt{33}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{33}}{2*-1}=\frac{-5+\sqrt{33}}{-2}
$