2(x+3)5x=12

Solution for 2(x+3)5x=12 equation:

2(x+3)5x=12

We move all terms to the left:

2(x+3)5x-(12)=0

We multiply parentheses

10x^2+30x-12=0

a = 10; b = 30; c = -12;
Δ = b2-4ac
Δ = 302-4·10·(-12)
Δ = 1380
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:

$\sqrt{\Delta}=\sqrt{1380}=\sqrt{4*345}=\sqrt{4}*\sqrt{345}=2\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{345}}{2*10}=\frac{-30-2\sqrt{345}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{345}}{2*10}=\frac{-30+2\sqrt{345}}{20}
$