(6x+100)10x=180

Solution for (6x+100)10x=180 equation:

(6x+100)10x=180

We move all terms to the left:

(6x+100)10x-(180)=0

We multiply parentheses

60x^2+1000x-180=0

a = 60; b = 1000; c = -180;
Δ = b2-4ac
Δ = 10002-4·60·(-180)
Δ = 1043200
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:

$\sqrt{\Delta}=\sqrt{1043200}=\sqrt{6400*163}=\sqrt{6400}*\sqrt{163}=80\sqrt{163}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1000)-80\sqrt{163}}{2*60}=\frac{-1000-80\sqrt{163}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1000)+80\sqrt{163}}{2*60}=\frac{-1000+80\sqrt{163}}{120}
$