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

Solution for 6(x+2)=2(2x+15)3x equation:

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

We move all terms to the left:

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

We multiply parentheses

6x-(2(2x+15)3x)+12=0


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

2(2x+15)3x

We multiply parentheses

12x^2+90x

Back to the equation:

-(12x^2+90x)


We get rid of parentheses

-12x^2+6x-90x+12=0

We add all the numbers together, and all the variables

-12x^2-84x+12=0

a = -12; b = -84; c = +12;
Δ = b2-4ac
Δ = -842-4·(-12)·12
Δ = 7632
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:

$\sqrt{\Delta}=\sqrt{7632}=\sqrt{144*53}=\sqrt{144}*\sqrt{53}=12\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-12\sqrt{53}}{2*-12}=\frac{84-12\sqrt{53}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+12\sqrt{53}}{2*-12}=\frac{84+12\sqrt{53}}{-24}
$