6x+(2/3)x=180

Solution for 6x+(2/3)x=180 equation:

6x+(2/3)x=180

We move all terms to the left:

6x+(2/3)x-(180)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x+(+2/3)x-180=0

We multiply parentheses

2x^2+6x-180=0

a = 2; b = 6; c = -180;
Δ = b2-4ac
Δ = 62-4·2·(-180)
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{41}}{2*2}=\frac{-6-6\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{41}}{2*2}=\frac{-6+6\sqrt{41}}{4}
$