3x-10/4x+1=6

Solution for 3x-10/4x+1=6 equation:

3x-10/4x+1=6

We move all terms to the left:

3x-10/4x+1-(6)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3x-10/4x-5=0

We multiply all the terms by the denominator


3x*4x-5*4x-10=0

Wy multiply elements

12x^2-20x-10=0

a = 12; b = -20; c = -10;
Δ = b2-4ac
Δ = -202-4·12·(-10)
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{55}}{2*12}=\frac{20-4\sqrt{55}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{55}}{2*12}=\frac{20+4\sqrt{55}}{24}
$