5+5/7x=4x+28

Solution for 5+5/7x=4x+28 equation:

5+5/7x=4x+28

We move all terms to the left:

5+5/7x-(4x+28)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

5/7x-4x-28+5=0

We multiply all the terms by the denominator


-4x*7x-28*7x+5*7x+5=0

Wy multiply elements

-28x^2-196x+35x+5=0

We add all the numbers together, and all the variables

-28x^2-161x+5=0

a = -28; b = -161; c = +5;
Δ = b2-4ac
Δ = -1612-4·(-28)·5
Δ = 26481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-161)-\sqrt{26481}}{2*-28}=\frac{161-\sqrt{26481}}{-56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-161)+\sqrt{26481}}{2*-28}=\frac{161+\sqrt{26481}}{-56}
$