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

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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 $

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