x(2x+1)/3=5

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

x(2x+1)/3=5

We move all terms to the left:

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x(2x+1)-15=0

We multiply parentheses

2x^2+x-15=0

a = 2; b = 1; c = -15;
Δ = b2-4ac
Δ = 12-4·2·(-15)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-11}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*2}=\frac{10}{4}
=2+1/2
$