X+12=1/2xx+20

Solution for X+12=1/2xx+20 equation:

X+12=1/2XX+20

We move all terms to the left:

X+12-(1/2XX+20)=0


Domain of the equation: 2XX+20)!=0

X∈R


We get rid of parentheses

X-1/2XX-20+12=0

We multiply all the terms by the denominator


X*2XX-20*2XX+12*2XX-1=0

Wy multiply elements

2X^2-40X+24X-1=0

We add all the numbers together, and all the variables

2X^2-16X-1=0

a = 2; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·2·(-1)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{66}}{2*2}=\frac{16-2\sqrt{66}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{66}}{2*2}=\frac{16+2\sqrt{66}}{4}
$