1/2X+4=-3.5x+20

Solution for 1/2X+4=-3.5x+20 equation:

1/2X+4=-3.5X+20

We move all terms to the left:

1/2X+4-(-3.5X+20)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We get rid of parentheses

1/2X+3.5X-20+4=0

We multiply all the terms by the denominator


(3.5X)*2X-20*2X+4*2X+1=0

We add all the numbers together, and all the variables

(+3.5X)*2X-20*2X+4*2X+1=0

We multiply parentheses

6X^2-20*2X+4*2X+1=0

Wy multiply elements

6X^2-40X+8X+1=0

We add all the numbers together, and all the variables

6X^2-32X+1=0

a = 6; b = -32; c = +1;
Δ = b2-4ac
Δ = -322-4·6·1
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-10\sqrt{10}}{2*6}=\frac{32-10\sqrt{10}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+10\sqrt{10}}{2*6}=\frac{32+10\sqrt{10}}{12}
$