x-8/3x=110

Solution for x-8/3x=110 equation:

x-8/3x=110

We move all terms to the left:

x-8/3x-(110)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-110*3x-8=0

Wy multiply elements

3x^2-330x-8=0

a = 3; b = -330; c = -8;
Δ = b2-4ac
Δ = -3302-4·3·(-8)
Δ = 108996
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:

$\sqrt{\Delta}=\sqrt{108996}=\sqrt{4*27249}=\sqrt{4}*\sqrt{27249}=2\sqrt{27249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-330)-2\sqrt{27249}}{2*3}=\frac{330-2\sqrt{27249}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-330)+2\sqrt{27249}}{2*3}=\frac{330+2\sqrt{27249}}{6}
$