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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(3x(x-1)+x(x+5)), so:

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

We multiply parentheses

3x^2+x^2-3x+5x

We add all the numbers together, and all the variables

4x^2+2x

Back to the equation:

-(4x^2+2x)


We get rid of parentheses

-4x^2+2x-2x+1=0

We add all the numbers together, and all the variables

-4x^2+1=0

a = -4; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-4)·1
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*-4}=\frac{-4}{-8}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*-4}=\frac{4}{-8}
=-1/2
$