5x-1=5/3x+4=2

Solution for 5x-1=5/3x+4=2 equation:

5x-1=5/3x+4=2

We move all terms to the left:

5x-1-(5/3x+4)=0


Domain of the equation: 3x+4)!=0

x∈R


We get rid of parentheses

5x-5/3x-4-1=0

We multiply all the terms by the denominator


5x*3x-4*3x-1*3x-5=0

Wy multiply elements

15x^2-12x-3x-5=0

We add all the numbers together, and all the variables

15x^2-15x-5=0

a = 15; b = -15; c = -5;
Δ = b2-4ac
Δ = -152-4·15·(-5)
Δ = 525
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:

$\sqrt{\Delta}=\sqrt{525}=\sqrt{25*21}=\sqrt{25}*\sqrt{21}=5\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{21}}{2*15}=\frac{15-5\sqrt{21}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{21}}{2*15}=\frac{15+5\sqrt{21}}{30}
$