2(3x-10)2x=100

Solution for 2(3x-10)2x=100 equation:

2(3x-10)2x=100

We move all terms to the left:

2(3x-10)2x-(100)=0

We multiply parentheses

12x^2-40x-100=0

a = 12; b = -40; c = -100;
Δ = b2-4ac
Δ = -402-4·12·(-100)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-80}{2*12}=\frac{-40}{24}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+80}{2*12}=\frac{120}{24}
=5
$