3x(x-4)+15=2(x+3)

Solution for 3x(x-4)+15=2(x+3) equation:

3x(x-4)+15=2(x+3)

We move all terms to the left:

3x(x-4)+15-(2(x+3))=0

We multiply parentheses

3x^2-12x-(2(x+3))+15=0


We calculate terms in parentheses: -(2(x+3)), so:

2(x+3)

We multiply parentheses

2x+6

Back to the equation:

-(2x+6)


We get rid of parentheses

3x^2-12x-2x-6+15=0

We add all the numbers together, and all the variables

3x^2-14x+9=0

a = 3; b = -14; c = +9;
Δ = b2-4ac
Δ = -142-4·3·9
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{22}}{2*3}=\frac{14-2\sqrt{22}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{22}}{2*3}=\frac{14+2\sqrt{22}}{6}
$