6/5x+x=66

Solution for 6/5x+x=66 equation:

6/5x+x=66

We move all terms to the left:

6/5x+x-(66)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x+6/5x-66=0

We multiply all the terms by the denominator


x*5x-66*5x+6=0

Wy multiply elements

5x^2-330x+6=0

a = 5; b = -330; c = +6;
Δ = b2-4ac
Δ = -3302-4·5·6
Δ = 108780
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:

$\sqrt{\Delta}=\sqrt{108780}=\sqrt{196*555}=\sqrt{196}*\sqrt{555}=14\sqrt{555}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-330)-14\sqrt{555}}{2*5}=\frac{330-14\sqrt{555}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-330)+14\sqrt{555}}{2*5}=\frac{330+14\sqrt{555}}{10}
$