X+1/2x+10=55

Solution for X+1/2x+10=55 equation:

X+1/2X+10=55

We move all terms to the left:

X+1/2X+10-(55)=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+1/2X-45=0

We multiply all the terms by the denominator


X*2X-45*2X+1=0

Wy multiply elements

2X^2-90X+1=0

a = 2; b = -90; c = +1;
Δ = b2-4ac
Δ = -902-4·2·1
Δ = 8092
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:

$\sqrt{\Delta}=\sqrt{8092}=\sqrt{1156*7}=\sqrt{1156}*\sqrt{7}=34\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-34\sqrt{7}}{2*2}=\frac{90-34\sqrt{7}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+34\sqrt{7}}{2*2}=\frac{90+34\sqrt{7}}{4}
$