3x=11/5x+4

Solution for 3x=11/5x+4 equation:

3x=11/5x+4

We move all terms to the left:

3x-(11/5x+4)=0


Domain of the equation: 5x+4)!=0

x∈R


We get rid of parentheses

3x-11/5x-4=0

We multiply all the terms by the denominator


3x*5x-4*5x-11=0

Wy multiply elements

15x^2-20x-11=0

a = 15; b = -20; c = -11;
Δ = b2-4ac
Δ = -202-4·15·(-11)
Δ = 1060
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:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{265}}{2*15}=\frac{20-2\sqrt{265}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{265}}{2*15}=\frac{20+2\sqrt{265}}{30}
$