X+5/6x+4/6x=150

Solution for X+5/6x+4/6x=150 equation:

X+5/6X+4/6X=150

We move all terms to the left:

X+5/6X+4/6X-(150)=0


Domain of the equation: 6X!=0

X!=0/6

X!=0

X∈R


We multiply all the terms by the denominator


X*6X-150*6X+5+4=0

We add all the numbers together, and all the variables

X*6X-150*6X+9=0

Wy multiply elements

6X^2-900X+9=0

a = 6; b = -900; c = +9;
Δ = b2-4ac
Δ = -9002-4·6·9
Δ = 809784
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:

$\sqrt{\Delta}=\sqrt{809784}=\sqrt{36*22494}=\sqrt{36}*\sqrt{22494}=6\sqrt{22494}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-6\sqrt{22494}}{2*6}=\frac{900-6\sqrt{22494}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+6\sqrt{22494}}{2*6}=\frac{900+6\sqrt{22494}}{12}
$