(3x+50)6x-10=180

Solution for (3x+50)6x-10=180 equation:

(3x+50)6x-10=180

We move all terms to the left:

(3x+50)6x-10-(180)=0

We add all the numbers together, and all the variables

(3x+50)6x-190=0

We multiply parentheses

18x^2+300x-190=0

a = 18; b = 300; c = -190;
Δ = b2-4ac
Δ = 3002-4·18·(-190)
Δ = 103680
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:

$\sqrt{\Delta}=\sqrt{103680}=\sqrt{20736*5}=\sqrt{20736}*\sqrt{5}=144\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-144\sqrt{5}}{2*18}=\frac{-300-144\sqrt{5}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+144\sqrt{5}}{2*18}=\frac{-300+144\sqrt{5}}{36}
$