3x+4/2x-10=11

Solution for 3x+4/2x-10=11 equation:

3x+4/2x-10=11

We move all terms to the left:

3x+4/2x-10-(11)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+4/2x-21=0

We multiply all the terms by the denominator


3x*2x-21*2x+4=0

Wy multiply elements

6x^2-42x+4=0

a = 6; b = -42; c = +4;
Δ = b2-4ac
Δ = -422-4·6·4
Δ = 1668
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:

$\sqrt{\Delta}=\sqrt{1668}=\sqrt{4*417}=\sqrt{4}*\sqrt{417}=2\sqrt{417}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{417}}{2*6}=\frac{42-2\sqrt{417}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{417}}{2*6}=\frac{42+2\sqrt{417}}{12}
$