(6x+4)100x=180

Solution for (6x+4)100x=180 equation:

(6x+4)100x=180

We move all terms to the left:

(6x+4)100x-(180)=0

We multiply parentheses

600x^2+400x-180=0

a = 600; b = 400; c = -180;
Δ = b2-4ac
Δ = 4002-4·600·(-180)
Δ = 592000
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:

$\sqrt{\Delta}=\sqrt{592000}=\sqrt{1600*370}=\sqrt{1600}*\sqrt{370}=40\sqrt{370}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-40\sqrt{370}}{2*600}=\frac{-400-40\sqrt{370}}{1200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+40\sqrt{370}}{2*600}=\frac{-400+40\sqrt{370}}{1200}
$