7x-3/5x=2

Solution for 7x-3/5x=2 equation:

7x-3/5x=2

We move all terms to the left:

7x-3/5x-(2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


7x*5x-2*5x-3=0

Wy multiply elements

35x^2-10x-3=0

a = 35; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·35·(-3)
Δ = 520
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:

$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{130}}{2*35}=\frac{10-2\sqrt{130}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{130}}{2*35}=\frac{10+2\sqrt{130}}{70}
$