(3/2x+2)+(5/4x+6)=180

Solution for (3/2x+2)+(5/4x+6)=180 equation:

(3/2x+2)+(5/4x+6)=180

We move all terms to the left:

(3/2x+2)+(5/4x+6)-(180)=0


Domain of the equation: 2x+2)!=0

x∈R



Domain of the equation: 4x+6)!=0

x∈R


We get rid of parentheses

3/2x+5/4x+2+6-180=0

We calculate fractions


12x/8x^2+10x/8x^2+2+6-180=0

We add all the numbers together, and all the variables

12x/8x^2+10x/8x^2-172=0

We multiply all the terms by the denominator


12x+10x-172*8x^2=0

We add all the numbers together, and all the variables

22x-172*8x^2=0

Wy multiply elements

-1376x^2+22x=0

a = -1376; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-1376)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-1376}=\frac{-44}{-2752}
=11/688
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-1376}=\frac{0}{-2752}
=0
$