5x-3/2x=5

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

5x-3/2x=5

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

10x^2-10x-3=0

a = 10; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·10·(-3)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{55}}{2*10}=\frac{10-2\sqrt{55}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{55}}{2*10}=\frac{10+2\sqrt{55}}{20}
$