x-(1/2x+5)=31

Solution for x-(1/2x+5)=31 equation:

x-(1/2x+5)=31

We move all terms to the left:

x-(1/2x+5)-(31)=0


Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

x-1/2x-5-31=0

We multiply all the terms by the denominator


x*2x-5*2x-31*2x-1=0

Wy multiply elements

2x^2-10x-62x-1=0

We add all the numbers together, and all the variables

2x^2-72x-1=0

a = 2; b = -72; c = -1;
Δ = b2-4ac
Δ = -722-4·2·(-1)
Δ = 5192
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:

$\sqrt{\Delta}=\sqrt{5192}=\sqrt{4*1298}=\sqrt{4}*\sqrt{1298}=2\sqrt{1298}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1298}}{2*2}=\frac{72-2\sqrt{1298}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1298}}{2*2}=\frac{72+2\sqrt{1298}}{4}
$