X+2x-4+5/6x=157

Solution for X+2x-4+5/6x=157 equation:

X+2X-4+5/6X=157

We move all terms to the left:

X+2X-4+5/6X-(157)=0


Domain of the equation: 6X!=0

X!=0/6

X!=0

X∈R


We add all the numbers together, and all the variables

3X+5/6X-161=0

We multiply all the terms by the denominator


3X*6X-161*6X+5=0

Wy multiply elements

18X^2-966X+5=0

a = 18; b = -966; c = +5;
Δ = b2-4ac
Δ = -9662-4·18·5
Δ = 932796
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:

$\sqrt{\Delta}=\sqrt{932796}=\sqrt{324*2879}=\sqrt{324}*\sqrt{2879}=18\sqrt{2879}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-966)-18\sqrt{2879}}{2*18}=\frac{966-18\sqrt{2879}}{36}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-966)+18\sqrt{2879}}{2*18}=\frac{966+18\sqrt{2879}}{36}
$