2x(x+2)/3=1

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

2x(x+2)/3=1

We move all terms to the left:

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x(x+2)-3=0

We multiply parentheses

2x^2+4x-3=0

a = 2; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·2·(-3)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{10}}{2*2}=\frac{-4-2\sqrt{10}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{10}}{2*2}=\frac{-4+2\sqrt{10}}{4}
$