(7/4x+10)+(2x+15)+(5/4x+20)+(3/4x+5)=180

Solution for (7/4x+10)+(2x+15)+(5/4x+20)+(3/4x+5)=180 equation:

(7/4x+10)+(2x+15)+(5/4x+20)+(3/4x+5)=180

We move all terms to the left:

(7/4x+10)+(2x+15)+(5/4x+20)+(3/4x+5)-(180)=0


Domain of the equation: 4x+10)!=0

x∈R



Domain of the equation: 4x+20)!=0

x∈R



Domain of the equation: 4x+5)!=0

x∈R


We get rid of parentheses

7/4x+2x+5/4x+3/4x+10+15+20+5-180=0

We multiply all the terms by the denominator


2x*4x+10*4x+15*4x+20*4x+5*4x-180*4x+7+5+3=0

We add all the numbers together, and all the variables

2x*4x+10*4x+15*4x+20*4x+5*4x-180*4x+15=0

Wy multiply elements

8x^2+40x+60x+80x+20x-720x+15=0

We add all the numbers together, and all the variables

8x^2-520x+15=0

a = 8; b = -520; c = +15;
Δ = b2-4ac
Δ = -5202-4·8·15
Δ = 269920
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:

$\sqrt{\Delta}=\sqrt{269920}=\sqrt{16*16870}=\sqrt{16}*\sqrt{16870}=4\sqrt{16870}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-520)-4\sqrt{16870}}{2*8}=\frac{520-4\sqrt{16870}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-520)+4\sqrt{16870}}{2*8}=\frac{520+4\sqrt{16870}}{16}
$