(x)=1/2x+13

Solution for (x)=1/2x+13 equation:

(x)=1/2x+13

We move all terms to the left:

(x)-(1/2x+13)=0


Domain of the equation: 2x+13)!=0

x∈R


We get rid of parentheses

x-1/2x-13=0

We multiply all the terms by the denominator


x*2x-13*2x-1=0

Wy multiply elements

2x^2-26x-1=0

a = 2; b = -26; c = -1;
Δ = b2-4ac
Δ = -262-4·2·(-1)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-6\sqrt{19}}{2*2}=\frac{26-6\sqrt{19}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+6\sqrt{19}}{2*2}=\frac{26+6\sqrt{19}}{4}
$