5x-7/5x=2

Solution for 5x-7/5x=2 equation:

5x-7/5x=2

We move all terms to the left:

5x-7/5x-(2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


5x*5x-2*5x-7=0

Wy multiply elements

25x^2-10x-7=0

a = 25; b = -10; c = -7;
Δ = b2-4ac
Δ = -102-4·25·(-7)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-20\sqrt{2}}{2*25}=\frac{10-20\sqrt{2}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+20\sqrt{2}}{2*25}=\frac{10+20\sqrt{2}}{50}
$