X+31/2x+10=46

Solution for X+31/2x+10=46 equation:

X+31/2X+10=46

We move all terms to the left:

X+31/2X+10-(46)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

X+31/2X-36=0

We multiply all the terms by the denominator


X*2X-36*2X+31=0

Wy multiply elements

2X^2-72X+31=0

a = 2; b = -72; c = +31;
Δ = b2-4ac
Δ = -722-4·2·31
Δ = 4936
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:

$\sqrt{\Delta}=\sqrt{4936}=\sqrt{4*1234}=\sqrt{4}*\sqrt{1234}=2\sqrt{1234}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1234}}{2*2}=\frac{72-2\sqrt{1234}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1234}}{2*2}=\frac{72+2\sqrt{1234}}{4}
$