4x-12/5x=2

Solution for 4x-12/5x=2 equation:

4x-12/5x=2

We move all terms to the left:

4x-12/5x-(2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


4x*5x-2*5x-12=0

Wy multiply elements

20x^2-10x-12=0

a = 20; b = -10; c = -12;
Δ = b2-4ac
Δ = -102-4·20·(-12)
Δ = 1060
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:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{265}}{2*20}=\frac{10-2\sqrt{265}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{265}}{2*20}=\frac{10+2\sqrt{265}}{40}
$