13x-6=1/2x+7

Solution for 13x-6=1/2x+7 equation:

13x-6=1/2x+7

We move all terms to the left:

13x-6-(1/2x+7)=0


Domain of the equation: 2x+7)!=0

x∈R


We get rid of parentheses

13x-1/2x-7-6=0

We multiply all the terms by the denominator


13x*2x-7*2x-6*2x-1=0

Wy multiply elements

26x^2-14x-12x-1=0

We add all the numbers together, and all the variables

26x^2-26x-1=0

a = 26; b = -26; c = -1;
Δ = b2-4ac
Δ = -262-4·26·(-1)
Δ = 780
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:

$\sqrt{\Delta}=\sqrt{780}=\sqrt{4*195}=\sqrt{4}*\sqrt{195}=2\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{195}}{2*26}=\frac{26-2\sqrt{195}}{52}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{195}}{2*26}=\frac{26+2\sqrt{195}}{52}
$