3x(x+7)=2(3x+15)

Solution for 3x(x+7)=2(3x+15) equation:

3x(x+7)=2(3x+15)

We move all terms to the left:

3x(x+7)-(2(3x+15))=0

We multiply parentheses

3x^2+21x-(2(3x+15))=0


We calculate terms in parentheses: -(2(3x+15)), so:

2(3x+15)

We multiply parentheses

6x+30

Back to the equation:

-(6x+30)


We get rid of parentheses

3x^2+21x-6x-30=0

We add all the numbers together, and all the variables

3x^2+15x-30=0

a = 3; b = 15; c = -30;
Δ = b2-4ac
Δ = 152-4·3·(-30)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{65}}{2*3}=\frac{-15-3\sqrt{65}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{65}}{2*3}=\frac{-15+3\sqrt{65}}{6}
$