X+7/3x=120

Solution for X+7/3x=120 equation:

X+7/3X=120

We move all terms to the left:

X+7/3X-(120)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-120*3X+7=0

Wy multiply elements

3X^2-360X+7=0

a = 3; b = -360; c = +7;
Δ = b2-4ac
Δ = -3602-4·3·7
Δ = 129516
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:

$\sqrt{\Delta}=\sqrt{129516}=\sqrt{4*32379}=\sqrt{4}*\sqrt{32379}=2\sqrt{32379}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-2\sqrt{32379}}{2*3}=\frac{360-2\sqrt{32379}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+2\sqrt{32379}}{2*3}=\frac{360+2\sqrt{32379}}{6}
$