4x-14/7x=-7

Solution for 4x-14/7x=-7 equation:

4x-14/7x=-7

We move all terms to the left:

4x-14/7x-(-7)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

4x-14/7x+7=0

We multiply all the terms by the denominator


4x*7x+7*7x-14=0

Wy multiply elements

28x^2+49x-14=0

a = 28; b = 49; c = -14;
Δ = b2-4ac
Δ = 492-4·28·(-14)
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-63}{2*28}=\frac{-112}{56}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+63}{2*28}=\frac{14}{56}
=1/4
$