(5x^2)/(2x)=6

Solution for (5x^2)/(2x)=6 equation:

(5x^2)/(2x)=6

We move all terms to the left:

(5x^2)/(2x)-(6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


5x^2-6*2x=0

Wy multiply elements

5x^2-12x=0

a = 5; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·5·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*5}=\frac{24}{10}
=2+2/5
$