3x+4/7x-3=5

Solution for 3x+4/7x-3=5 equation:

3x+4/7x-3=5

We move all terms to the left:

3x+4/7x-3-(5)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

3x+4/7x-8=0

We multiply all the terms by the denominator


3x*7x-8*7x+4=0

Wy multiply elements

21x^2-56x+4=0

a = 21; b = -56; c = +4;
Δ = b2-4ac
Δ = -562-4·21·4
Δ = 2800
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:

$\sqrt{\Delta}=\sqrt{2800}=\sqrt{400*7}=\sqrt{400}*\sqrt{7}=20\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-20\sqrt{7}}{2*21}=\frac{56-20\sqrt{7}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+20\sqrt{7}}{2*21}=\frac{56+20\sqrt{7}}{42}
$