2x+x+(3/2)x+45=180

Solution for 2x+x+(3/2)x+45=180 equation:

2x+x+(3/2)x+45=180

We move all terms to the left:

2x+x+(3/2)x+45-(180)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x+x+(+3/2)x+45-180=0

We add all the numbers together, and all the variables

3x+(+3/2)x-135=0

We multiply parentheses

3x^2+3x-135=0

a = 3; b = 3; c = -135;
Δ = b2-4ac
Δ = 32-4·3·(-135)
Δ = 1629
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:

$\sqrt{\Delta}=\sqrt{1629}=\sqrt{9*181}=\sqrt{9}*\sqrt{181}=3\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{181}}{2*3}=\frac{-3-3\sqrt{181}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{181}}{2*3}=\frac{-3+3\sqrt{181}}{6}
$