X+4/3x=56

Solution for X+4/3x=56 equation:

X+4/3X=56

We move all terms to the left:

X+4/3X-(56)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-56*3X+4=0

Wy multiply elements

3X^2-168X+4=0

a = 3; b = -168; c = +4;
Δ = b2-4ac
Δ = -1682-4·3·4
Δ = 28176
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:

$\sqrt{\Delta}=\sqrt{28176}=\sqrt{16*1761}=\sqrt{16}*\sqrt{1761}=4\sqrt{1761}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-4\sqrt{1761}}{2*3}=\frac{168-4\sqrt{1761}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+4\sqrt{1761}}{2*3}=\frac{168+4\sqrt{1761}}{6}
$