23/4x+13=7x-55

Solution for 23/4x+13=7x-55 equation:

23/4x+13=7x-55

We move all terms to the left:

23/4x+13-(7x-55)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

23/4x-7x+55+13=0

We multiply all the terms by the denominator


-7x*4x+55*4x+13*4x+23=0

Wy multiply elements

-28x^2+220x+52x+23=0

We add all the numbers together, and all the variables

-28x^2+272x+23=0

a = -28; b = 272; c = +23;
Δ = b2-4ac
Δ = 2722-4·(-28)·23
Δ = 76560
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:

$\sqrt{\Delta}=\sqrt{76560}=\sqrt{16*4785}=\sqrt{16}*\sqrt{4785}=4\sqrt{4785}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(272)-4\sqrt{4785}}{2*-28}=\frac{-272-4\sqrt{4785}}{-56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(272)+4\sqrt{4785}}{2*-28}=\frac{-272+4\sqrt{4785}}{-56}
$