X-14+1/2x+7+3x-83=180

Solution for X-14+1/2x+7+3x-83=180 equation:

X-14+1/2X+7+3X-83=180

We move all terms to the left:

X-14+1/2X+7+3X-83-(180)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

4X+1/2X-270=0

We multiply all the terms by the denominator


4X*2X-270*2X+1=0

Wy multiply elements

8X^2-540X+1=0

a = 8; b = -540; c = +1;
Δ = b2-4ac
Δ = -5402-4·8·1
Δ = 291568
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:

$\sqrt{\Delta}=\sqrt{291568}=\sqrt{16*18223}=\sqrt{16}*\sqrt{18223}=4\sqrt{18223}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-4\sqrt{18223}}{2*8}=\frac{540-4\sqrt{18223}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+4\sqrt{18223}}{2*8}=\frac{540+4\sqrt{18223}}{16}
$