X+2/3x+10=180

Solution for X+2/3x+10=180 equation:

X+2/3X+10=180

We move all terms to the left:

X+2/3X+10-(180)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X+2/3X-170=0

We multiply all the terms by the denominator


X*3X-170*3X+2=0

Wy multiply elements

3X^2-510X+2=0

a = 3; b = -510; c = +2;
Δ = b2-4ac
Δ = -5102-4·3·2
Δ = 260076
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:

$\sqrt{\Delta}=\sqrt{260076}=\sqrt{4*65019}=\sqrt{4}*\sqrt{65019}=2\sqrt{65019}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-510)-2\sqrt{65019}}{2*3}=\frac{510-2\sqrt{65019}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-510)+2\sqrt{65019}}{2*3}=\frac{510+2\sqrt{65019}}{6}
$