x/7x-8=4x+19*

Solution for x/7x-8=4x+19* equation:

x/7x-8=4x+19*

We move all terms to the left:

x/7x-8-(4x+19*)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

x/7x-(+4x)-8=0

We get rid of parentheses

x/7x-4x-8=0

We multiply all the terms by the denominator


x-4x*7x-8*7x=0

Wy multiply elements

-28x^2+x-56x=0

We add all the numbers together, and all the variables

-28x^2-55x=0

a = -28; b = -55; c = 0;
Δ = b2-4ac
Δ = -552-4·(-28)·0
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-55}{2*-28}=\frac{0}{-56}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+55}{2*-28}=\frac{110}{-56}
=-1+27/28
$