(X+40)+(2/3x)=180

Solution for (X+40)+(2/3x)=180 equation:

(X+40)+(2/3X)=180

We move all terms to the left:

(X+40)+(2/3X)-(180)=0


Domain of the equation: 3X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

(X+40)+(+2/3X)-180=0

We get rid of parentheses

X+2/3X+40-180=0

We multiply all the terms by the denominator


X*3X+40*3X-180*3X+2=0

Wy multiply elements

3X^2+120X-540X+2=0

We add all the numbers together, and all the variables

3X^2-420X+2=0

a = 3; b = -420; c = +2;
Δ = b2-4ac
Δ = -4202-4·3·2
Δ = 176376
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:

$\sqrt{\Delta}=\sqrt{176376}=\sqrt{4*44094}=\sqrt{4}*\sqrt{44094}=2\sqrt{44094}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-2\sqrt{44094}}{2*3}=\frac{420-2\sqrt{44094}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+2\sqrt{44094}}{2*3}=\frac{420+2\sqrt{44094}}{6}
$