3x-15/2x=6

Solution for 3x-15/2x=6 equation:

3x-15/2x=6

We move all terms to the left:

3x-15/2x-(6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


3x*2x-6*2x-15=0

Wy multiply elements

6x^2-12x-15=0

a = 6; b = -12; c = -15;
Δ = b2-4ac
Δ = -122-4·6·(-15)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{14}}{2*6}=\frac{12-6\sqrt{14}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{14}}{2*6}=\frac{12+6\sqrt{14}}{12}
$