2x+40+800/x=150

Solution for 2x+40+800/x=150 equation:

2x+40+800/x=150

We move all terms to the left:

2x+40+800/x-(150)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x+800/x-110=0

We multiply all the terms by the denominator


2x*x-110*x+800=0

We add all the numbers together, and all the variables

-110x+2x*x+800=0

Wy multiply elements

2x^2-110x+800=0

a = 2; b = -110; c = +800;
Δ = b2-4ac
Δ = -1102-4·2·800
Δ = 5700
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:

$\sqrt{\Delta}=\sqrt{5700}=\sqrt{100*57}=\sqrt{100}*\sqrt{57}=10\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-10\sqrt{57}}{2*2}=\frac{110-10\sqrt{57}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+10\sqrt{57}}{2*2}=\frac{110+10\sqrt{57}}{4}
$