280/x+2=20+2.5x

Solution for 280/x+2=20+2.5x equation:

280/x+2=20+2.5x

We move all terms to the left:

280/x+2-(20+2.5x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

280/x-(2.5x+20)+2=0

We get rid of parentheses

280/x-2.5x-20+2=0

We multiply all the terms by the denominator


-(2.5x)*x-20*x+2*x+280=0

We add all the numbers together, and all the variables

-(+2.5x)*x-20*x+2*x+280=0

We add all the numbers together, and all the variables

-18x-(+2.5x)*x+280=0

We multiply parentheses

-2x^2-18x+280=0

a = -2; b = -18; c = +280;
Δ = b2-4ac
Δ = -182-4·(-2)·280
Δ = 2564
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:

$\sqrt{\Delta}=\sqrt{2564}=\sqrt{4*641}=\sqrt{4}*\sqrt{641}=2\sqrt{641}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{641}}{2*-2}=\frac{18-2\sqrt{641}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{641}}{2*-2}=\frac{18+2\sqrt{641}}{-4}
$