3/4x-13=x+7

Solution for 3/4x-13=x+7 equation:

3/4x-13=x+7

We move all terms to the left:

3/4x-13-(x+7)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-x-7-13=0

We multiply all the terms by the denominator


-x*4x-7*4x-13*4x+3=0

Wy multiply elements

-4x^2-28x-52x+3=0

We add all the numbers together, and all the variables

-4x^2-80x+3=0

a = -4; b = -80; c = +3;
Δ = b2-4ac
Δ = -802-4·(-4)·3
Δ = 6448
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:

$\sqrt{\Delta}=\sqrt{6448}=\sqrt{16*403}=\sqrt{16}*\sqrt{403}=4\sqrt{403}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{403}}{2*-4}=\frac{80-4\sqrt{403}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{403}}{2*-4}=\frac{80+4\sqrt{403}}{-8}
$