11/2x+15+x=190

Solution for 11/2x+15+x=190 equation:

11/2x+15+x=190

We move all terms to the left:

11/2x+15+x-(190)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+11/2x-175=0

We multiply all the terms by the denominator


x*2x-175*2x+11=0

Wy multiply elements

2x^2-350x+11=0

a = 2; b = -350; c = +11;
Δ = b2-4ac
Δ = -3502-4·2·11
Δ = 122412
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:

$\sqrt{\Delta}=\sqrt{122412}=\sqrt{40804*3}=\sqrt{40804}*\sqrt{3}=202\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-350)-202\sqrt{3}}{2*2}=\frac{350-202\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-350)+202\sqrt{3}}{2*2}=\frac{350+202\sqrt{3}}{4}
$