12(3x+7x)x=5

Solution for 12(3x+7x)x=5 equation:

12(3x+7x)x=5

We move all terms to the left:

12(3x+7x)x-(5)=0

We add all the numbers together, and all the variables

12(+10x)x-5=0

We multiply parentheses

120x^2-5=0

a = 120; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·120·(-5)
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{6}}{2*120}=\frac{0-20\sqrt{6}}{240}
=-\frac{20\sqrt{6}}{240}
=-\frac{\sqrt{6}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{6}}{2*120}=\frac{0+20\sqrt{6}}{240}
=\frac{20\sqrt{6}}{240}
=\frac{\sqrt{6}}{12}
$