5x-7/4x+7=14

Solution for 5x-7/4x+7=14 equation:

5x-7/4x+7=14

We move all terms to the left:

5x-7/4x+7-(14)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

5x-7/4x-7=0

We multiply all the terms by the denominator


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

Wy multiply elements

20x^2-28x-7=0

a = 20; b = -28; c = -7;
Δ = b2-4ac
Δ = -282-4·20·(-7)
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-8\sqrt{21}}{2*20}=\frac{28-8\sqrt{21}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+8\sqrt{21}}{2*20}=\frac{28+8\sqrt{21}}{40}
$