(1/2x)+106=180x=148

Solution for (1/2x)+106=180x=148 equation:

(1/2x)+106=180x=148

We move all terms to the left:

(1/2x)+106-(180x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2x)-180x+106=0

We add all the numbers together, and all the variables

-180x+(+1/2x)+106=0

We get rid of parentheses

-180x+1/2x+106=0

We multiply all the terms by the denominator


-180x*2x+106*2x+1=0

Wy multiply elements

-360x^2+212x+1=0

a = -360; b = 212; c = +1;
Δ = b2-4ac
Δ = 2122-4·(-360)·1
Δ = 46384
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:

$\sqrt{\Delta}=\sqrt{46384}=\sqrt{16*2899}=\sqrt{16}*\sqrt{2899}=4\sqrt{2899}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(212)-4\sqrt{2899}}{2*-360}=\frac{-212-4\sqrt{2899}}{-720}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(212)+4\sqrt{2899}}{2*-360}=\frac{-212+4\sqrt{2899}}{-720}
$