6x+31=1/219x-36

Solution for 6x+31=1/219x-36 equation:

6x+31=1/219x-36

We move all terms to the left:

6x+31-(1/219x-36)=0


Domain of the equation: 219x-36)!=0

x∈R


We get rid of parentheses

6x-1/219x+36+31=0

We multiply all the terms by the denominator


6x*219x+36*219x+31*219x-1=0

Wy multiply elements

1314x^2+7884x+6789x-1=0

We add all the numbers together, and all the variables

1314x^2+14673x-1=0

a = 1314; b = 14673; c = -1;
Δ = b2-4ac
Δ = 146732-4·1314·(-1)
Δ = 215302185
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:

$\sqrt{\Delta}=\sqrt{215302185}=\sqrt{9*23922465}=\sqrt{9}*\sqrt{23922465}=3\sqrt{23922465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14673)-3\sqrt{23922465}}{2*1314}=\frac{-14673-3\sqrt{23922465}}{2628}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14673)+3\sqrt{23922465}}{2*1314}=\frac{-14673+3\sqrt{23922465}}{2628}
$