7x-5/4x=3

Solution for 7x-5/4x=3 equation:

7x-5/4x=3

We move all terms to the left:

7x-5/4x-(3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


7x*4x-3*4x-5=0

Wy multiply elements

28x^2-12x-5=0

a = 28; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·28·(-5)
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{11}}{2*28}=\frac{12-8\sqrt{11}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{11}}{2*28}=\frac{12+8\sqrt{11}}{56}
$