X+4/3x=420

Solution for X+4/3x=420 equation:

X+4/3X=420

We move all terms to the left:

X+4/3X-(420)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-420*3X+4=0

Wy multiply elements

3X^2-1260X+4=0

a = 3; b = -1260; c = +4;
Δ = b2-4ac
Δ = -12602-4·3·4
Δ = 1587552
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:

$\sqrt{\Delta}=\sqrt{1587552}=\sqrt{16*99222}=\sqrt{16}*\sqrt{99222}=4\sqrt{99222}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1260)-4\sqrt{99222}}{2*3}=\frac{1260-4\sqrt{99222}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1260)+4\sqrt{99222}}{2*3}=\frac{1260+4\sqrt{99222}}{6}
$