1/2.x+2x=180-135

Solution for 1/2.x+2x=180-135 equation:

1/2.x+2x=180-135

We move all terms to the left:

1/2.x+2x-(180-135)=0


Domain of the equation: 2.x!=0

x!=0/2.

x!=0

x∈R


We add all the numbers together, and all the variables

1/2.x+2x-45=0

We add all the numbers together, and all the variables

2x+1/2.x-45=0

We multiply all the terms by the denominator


2x*2.x-45*2.x+1=0

Wy multiply elements

4x^2-90x+1=0

a = 4; b = -90; c = +1;
Δ = b2-4ac
Δ = -902-4·4·1
Δ = 8084
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:

$\sqrt{\Delta}=\sqrt{8084}=\sqrt{4*2021}=\sqrt{4}*\sqrt{2021}=2\sqrt{2021}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2021}}{2*4}=\frac{90-2\sqrt{2021}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2021}}{2*4}=\frac{90+2\sqrt{2021}}{8}
$