5x+2-3/2x-2=0

Solution for 5x+2-3/2x-2=0 equation:

5x+2-3/2x-2=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5x-3/2x=0

We multiply all the terms by the denominator


5x*2x-3=0

Wy multiply elements

10x^2-3=0

a = 10; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·10·(-3)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*10}=\frac{0-2\sqrt{30}}{20}
=-\frac{2\sqrt{30}}{20}
=-\frac{\sqrt{30}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*10}=\frac{0+2\sqrt{30}}{20}
=\frac{2\sqrt{30}}{20}
=\frac{\sqrt{30}}{10}
$