5x-5/3x=70

Solution for 5x-5/3x=70 equation:

5x-5/3x=70

We move all terms to the left:

5x-5/3x-(70)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


5x*3x-70*3x-5=0

Wy multiply elements

15x^2-210x-5=0

a = 15; b = -210; c = -5;
Δ = b2-4ac
Δ = -2102-4·15·(-5)
Δ = 44400
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:

$\sqrt{\Delta}=\sqrt{44400}=\sqrt{400*111}=\sqrt{400}*\sqrt{111}=20\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-20\sqrt{111}}{2*15}=\frac{210-20\sqrt{111}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+20\sqrt{111}}{2*15}=\frac{210+20\sqrt{111}}{30}
$