4x/3x+7=x-5/3x+7

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

4x/3x+7=x-5/3x+7

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x+7)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


4x-x*3x-7*3x+7*3x+5=0

Wy multiply elements

-3x^2+4x-21x+21x+5=0

We add all the numbers together, and all the variables

-3x^2+4x+5=0

a = -3; b = 4; c = +5;
Δ = b2-4ac
Δ = 42-4·(-3)·5
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{19}}{2*-3}=\frac{-4-2\sqrt{19}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{19}}{2*-3}=\frac{-4+2\sqrt{19}}{-6}
$