3x(x+2)=2(2x+7)

Solution for 3x(x+2)=2(2x+7) equation:

3x(x+2)=2(2x+7)

We move all terms to the left:

3x(x+2)-(2(2x+7))=0

We multiply parentheses

3x^2+6x-(2(2x+7))=0


We calculate terms in parentheses: -(2(2x+7)), so:

2(2x+7)

We multiply parentheses

4x+14

Back to the equation:

-(4x+14)


We get rid of parentheses

3x^2+6x-4x-14=0

We add all the numbers together, and all the variables

3x^2+2x-14=0

a = 3; b = 2; c = -14;
Δ = b2-4ac
Δ = 22-4·3·(-14)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{43}}{2*3}=\frac{-2-2\sqrt{43}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{43}}{2*3}=\frac{-2+2\sqrt{43}}{6}
$