3/7x+3x-42+2x-5=360

Solution for 3/7x+3x-42+2x-5=360 equation:

3/7x+3x-42+2x-5=360

We move all terms to the left:

3/7x+3x-42+2x-5-(360)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

5x+3/7x-407=0

We multiply all the terms by the denominator


5x*7x-407*7x+3=0

Wy multiply elements

35x^2-2849x+3=0

a = 35; b = -2849; c = +3;
Δ = b2-4ac
Δ = -28492-4·35·3
Δ = 8116381
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2849)-\sqrt{8116381}}{2*35}=\frac{2849-\sqrt{8116381}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2849)+\sqrt{8116381}}{2*35}=\frac{2849+\sqrt{8116381}}{70}
$