-2x+3/5x=0

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

-2x+3/5x=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


-2x*5x+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}
$