x-4/7x=21

Solution for x-4/7x=21 equation:

x-4/7x=21

We move all terms to the left:

x-4/7x-(21)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


x*7x-21*7x-4=0

Wy multiply elements

7x^2-147x-4=0

a = 7; b = -147; c = -4;
Δ = b2-4ac
Δ = -1472-4·7·(-4)
Δ = 21721
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{-(-147)-\sqrt{21721}}{2*7}=\frac{147-\sqrt{21721}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-147)+\sqrt{21721}}{2*7}=\frac{147+\sqrt{21721}}{14}
$