(2x-19)+(1/2x)=90

Solution for (2x-19)+(1/2x)=90 equation:

(2x-19)+(1/2x)=90

We move all terms to the left:

(2x-19)+(1/2x)-(90)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(2x-19)+(+1/2x)-90=0

We get rid of parentheses

2x+1/2x-19-90=0

We multiply all the terms by the denominator


2x*2x-19*2x-90*2x+1=0

Wy multiply elements

4x^2-38x-180x+1=0

We add all the numbers together, and all the variables

4x^2-218x+1=0

a = 4; b = -218; c = +1;
Δ = b2-4ac
Δ = -2182-4·4·1
Δ = 47508
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:

$\sqrt{\Delta}=\sqrt{47508}=\sqrt{4*11877}=\sqrt{4}*\sqrt{11877}=2\sqrt{11877}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-218)-2\sqrt{11877}}{2*4}=\frac{218-2\sqrt{11877}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-218)+2\sqrt{11877}}{2*4}=\frac{218+2\sqrt{11877}}{8}
$