4x-15/3x=+2

Solution for 4x-15/3x=+2 equation:

4x-15/3x=+2

We move all terms to the left:

4x-15/3x-(+2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4x-15/3x-2=0

We multiply all the terms by the denominator


4x*3x-2*3x-15=0

Wy multiply elements

12x^2-6x-15=0

a = 12; b = -6; c = -15;
Δ = b2-4ac
Δ = -62-4·12·(-15)
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{21}}{2*12}=\frac{6-6\sqrt{21}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{21}}{2*12}=\frac{6+6\sqrt{21}}{24}
$