3x-4=4(-10/3x)+14

Solution for 3x-4=4(-10/3x)+14 equation:

3x-4=4(-10/3x)+14

We move all terms to the left:

3x-4-(4(-10/3x)+14)=0


Domain of the equation: 3x)+14)!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


3x*3x)+14)-(4(-4*3x)+14)-10=0

Wy multiply elements

9x^2-12x=0

a = 9; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·9·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*9}=\frac{0}{18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*9}=\frac{24}{18}
=1+1/3
$