7/2x-3=x-13

Solution for 7/2x-3=x-13 equation:

7/2x-3=x-13

We move all terms to the left:

7/2x-3-(x-13)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

7/2x-x+13-3=0

We multiply all the terms by the denominator


-x*2x+13*2x-3*2x+7=0

Wy multiply elements

-2x^2+26x-6x+7=0

We add all the numbers together, and all the variables

-2x^2+20x+7=0

a = -2; b = 20; c = +7;
Δ = b2-4ac
Δ = 202-4·(-2)·7
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{114}}{2*-2}=\frac{-20-2\sqrt{114}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{114}}{2*-2}=\frac{-20+2\sqrt{114}}{-4}
$