4x-13=1/2x+13

Solution for 4x-13=1/2x+13 equation:

4x-13=1/2x+13

We move all terms to the left:

4x-13-(1/2x+13)=0


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

x∈R


We get rid of parentheses

4x-1/2x-13-13=0

We multiply all the terms by the denominator


4x*2x-13*2x-13*2x-1=0

Wy multiply elements

8x^2-26x-26x-1=0

We add all the numbers together, and all the variables

8x^2-52x-1=0

a = 8; b = -52; c = -1;
Δ = b2-4ac
Δ = -522-4·8·(-1)
Δ = 2736
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:

$\sqrt{\Delta}=\sqrt{2736}=\sqrt{144*19}=\sqrt{144}*\sqrt{19}=12\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-12\sqrt{19}}{2*8}=\frac{52-12\sqrt{19}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+12\sqrt{19}}{2*8}=\frac{52+12\sqrt{19}}{16}
$