3/7x+7/8x+3/8x=180

Solution for 3/7x+7/8x+3/8x=180 equation:

3/7x+7/8x+3/8x=180

We move all terms to the left:

3/7x+7/8x+3/8x-(180)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We calculate fractions


24x/56x^2+(21x+7)/56x^2-180=0

We multiply all the terms by the denominator


24x+(21x+7)-180*56x^2=0

Wy multiply elements

-10080x^2+24x+(21x+7)=0

We get rid of parentheses

-10080x^2+24x+21x+7=0

We add all the numbers together, and all the variables

-10080x^2+45x+7=0

a = -10080; b = 45; c = +7;
Δ = b2-4ac
Δ = 452-4·(-10080)·7
Δ = 284265
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:

$\sqrt{\Delta}=\sqrt{284265}=\sqrt{9*31585}=\sqrt{9}*\sqrt{31585}=3\sqrt{31585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{31585}}{2*-10080}=\frac{-45-3\sqrt{31585}}{-20160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{31585}}{2*-10080}=\frac{-45+3\sqrt{31585}}{-20160}
$