X+2x+(3/4)x=180

Solution for X+2x+(3/4)x=180 equation:

X+2X+(3/4)X=180

We move all terms to the left:

X+2X+(3/4)X-(180)=0


Domain of the equation: 4)X!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X+2X+(+3/4)X-180=0

We add all the numbers together, and all the variables

3X+(+3/4)X-180=0

We multiply parentheses

3X^2+3X-180=0

a = 3; b = 3; c = -180;
Δ = b2-4ac
Δ = 32-4·3·(-180)
Δ = 2169
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:

$\sqrt{\Delta}=\sqrt{2169}=\sqrt{9*241}=\sqrt{9}*\sqrt{241}=3\sqrt{241}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{241}}{2*3}=\frac{-3-3\sqrt{241}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{241}}{2*3}=\frac{-3+3\sqrt{241}}{6}
$