3x-4/7x+28=0

Solution for 3x-4/7x+28=0 equation:

3x-4/7x+28=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


3x*7x+28*7x-4=0

Wy multiply elements

21x^2+196x-4=0

a = 21; b = 196; c = -4;
Δ = b2-4ac
Δ = 1962-4·21·(-4)
Δ = 38752
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:

$\sqrt{\Delta}=\sqrt{38752}=\sqrt{16*2422}=\sqrt{16}*\sqrt{2422}=4\sqrt{2422}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(196)-4\sqrt{2422}}{2*21}=\frac{-196-4\sqrt{2422}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(196)+4\sqrt{2422}}{2*21}=\frac{-196+4\sqrt{2422}}{42}
$