2x(x+2)/3=21

Solution for 2x(x+2)/3=21 equation:

2x(x+2)/3=21

We move all terms to the left:

2x(x+2)/3-(21)=0

We multiply all the terms by the denominator


2x(x+2)-21*3=0

We add all the numbers together, and all the variables

2x(x+2)-63=0

We multiply parentheses

2x^2+4x-63=0

a = 2; b = 4; c = -63;
Δ = b2-4ac
Δ = 42-4·2·(-63)
Δ = 520
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:

$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{130}}{2*2}=\frac{-4-2\sqrt{130}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{130}}{2*2}=\frac{-4+2\sqrt{130}}{4}
$