1/2x+3+5(2)=x=5

Solution for 1/2x+3+5(2)=x=5 equation:

1/2x+3+5(2)=x=5

We move all terms to the left:

1/2x+3+5(2)-(x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/2x+55=0

We multiply all the terms by the denominator


-1x*2x+55*2x+1=0

Wy multiply elements

-2x^2+110x+1=0

a = -2; b = 110; c = +1;
Δ = b2-4ac
Δ = 1102-4·(-2)·1
Δ = 12108
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:

$\sqrt{\Delta}=\sqrt{12108}=\sqrt{4*3027}=\sqrt{4}*\sqrt{3027}=2\sqrt{3027}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-2\sqrt{3027}}{2*-2}=\frac{-110-2\sqrt{3027}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+2\sqrt{3027}}{2*-2}=\frac{-110+2\sqrt{3027}}{-4}
$