3x(x-2)=4(x+3)

Solution for 3x(x-2)=4(x+3) equation:

3x(x-2)=4(x+3)

We move all terms to the left:

3x(x-2)-(4(x+3))=0

We multiply parentheses

3x^2-6x-(4(x+3))=0


We calculate terms in parentheses: -(4(x+3)), so:

4(x+3)

We multiply parentheses

4x+12

Back to the equation:

-(4x+12)


We get rid of parentheses

3x^2-6x-4x-12=0

We add all the numbers together, and all the variables

3x^2-10x-12=0

a = 3; b = -10; c = -12;
Δ = b2-4ac
Δ = -102-4·3·(-12)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{61}}{2*3}=\frac{10-2\sqrt{61}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{61}}{2*3}=\frac{10+2\sqrt{61}}{6}
$