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

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

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

We move all terms to the left:

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

We multiply parentheses

6x^2+3x-(2(3x+1)+5)+5=0


We calculate terms in parentheses: -(2(3x+1)+5), so:

2(3x+1)+5

We multiply parentheses

6x+2+5

We add all the numbers together, and all the variables

6x+7

Back to the equation:

-(6x+7)


We get rid of parentheses

6x^2+3x-6x-7+5=0

We add all the numbers together, and all the variables

6x^2-3x-2=0

a = 6; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·6·(-2)
Δ = 57
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{-(-3)-\sqrt{57}}{2*6}=\frac{3-\sqrt{57}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{57}}{2*6}=\frac{3+\sqrt{57}}{12}
$