3x-7/4x=5

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

3x-7/4x=5

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-20x-7=0

a = 12; b = -20; c = -7;
Δ = b2-4ac
Δ = -202-4·12·(-7)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{46}}{2*12}=\frac{20-4\sqrt{46}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{46}}{2*12}=\frac{20+4\sqrt{46}}{24}
$