4/5x+x=36

Solution for 4/5x+x=36 equation:

4/5x+x=36

We move all terms to the left:

4/5x+x-(36)=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+4/5x-36=0

We multiply all the terms by the denominator


x*5x-36*5x+4=0

Wy multiply elements

5x^2-180x+4=0

a = 5; b = -180; c = +4;
Δ = b2-4ac
Δ = -1802-4·5·4
Δ = 32320
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:

$\sqrt{\Delta}=\sqrt{32320}=\sqrt{64*505}=\sqrt{64}*\sqrt{505}=8\sqrt{505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-8\sqrt{505}}{2*5}=\frac{180-8\sqrt{505}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+8\sqrt{505}}{2*5}=\frac{180+8\sqrt{505}}{10}
$