3x+12/2x-10=0

Solution for 3x+12/2x-10=0 equation:

3x+12/2x-10=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


3x*2x-10*2x+12=0

Wy multiply elements

6x^2-20x+12=0

a = 6; b = -20; c = +12;
Δ = b2-4ac
Δ = -202-4·6·12
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{7}}{2*6}=\frac{20-4\sqrt{7}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{7}}{2*6}=\frac{20+4\sqrt{7}}{12}
$