(1/5)x+(2/5)x=165

Solution for (1/5)x+(2/5)x=165 equation:

(1/5)x+(2/5)x=165

We move all terms to the left:

(1/5)x+(2/5)x-(165)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/5)x+(+2/5)x-165=0

We multiply parentheses

x^2+2x^2-165=0

We add all the numbers together, and all the variables

3x^2-165=0

a = 3; b = 0; c = -165;
Δ = b2-4ac
Δ = 02-4·3·(-165)
Δ = 1980
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:

$\sqrt{\Delta}=\sqrt{1980}=\sqrt{36*55}=\sqrt{36}*\sqrt{55}=6\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{55}}{2*3}=\frac{0-6\sqrt{55}}{6}
=-\frac{6\sqrt{55}}{6}
=-\sqrt{55}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{55}}{2*3}=\frac{0+6\sqrt{55}}{6}
=\frac{6\sqrt{55}}{6}
=\sqrt{55}
$