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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

12(+8x)x-7=0

We multiply parentheses

96x^2-7=0

a = 96; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·96·(-7)
Δ = 2688
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:

$\sqrt{\Delta}=\sqrt{2688}=\sqrt{64*42}=\sqrt{64}*\sqrt{42}=8\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{42}}{2*96}=\frac{0-8\sqrt{42}}{192}
=-\frac{8\sqrt{42}}{192}
=-\frac{\sqrt{42}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{42}}{2*96}=\frac{0+8\sqrt{42}}{192}
=\frac{8\sqrt{42}}{192}
=\frac{\sqrt{42}}{24}
$