7+x=13/4x

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

7+x=13/4x

We move all terms to the left:

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


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x-13/4x+7=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2+28x-13=0

a = 4; b = 28; c = -13;
Δ = b2-4ac
Δ = 282-4·4·(-13)
Δ = 992
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:

$\sqrt{\Delta}=\sqrt{992}=\sqrt{16*62}=\sqrt{16}*\sqrt{62}=4\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{62}}{2*4}=\frac{-28-4\sqrt{62}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{62}}{2*4}=\frac{-28+4\sqrt{62}}{8}
$