180=2/5x+2x

Solution for 180=2/5x+2x equation:

180=2/5x+2x

We move all terms to the left:

180-(2/5x+2x)=0


Domain of the equation: 5x+2x)!=0

x∈R


We add all the numbers together, and all the variables

-(+2x+2/5x)+180=0

We get rid of parentheses

-2x-2/5x+180=0

We multiply all the terms by the denominator


-2x*5x+180*5x-2=0

Wy multiply elements

-10x^2+900x-2=0

a = -10; b = 900; c = -2;
Δ = b2-4ac
Δ = 9002-4·(-10)·(-2)
Δ = 809920
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:

$\sqrt{\Delta}=\sqrt{809920}=\sqrt{64*12655}=\sqrt{64}*\sqrt{12655}=8\sqrt{12655}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(900)-8\sqrt{12655}}{2*-10}=\frac{-900-8\sqrt{12655}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(900)+8\sqrt{12655}}{2*-10}=\frac{-900+8\sqrt{12655}}{-20}
$