7x+3/4x-5=0

Solution for 7x+3/4x-5=0 equation:

7x+3/4x-5=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

28x^2-20x+3=0

a = 28; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·28·3
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8}{2*28}=\frac{12}{56}
=3/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8}{2*28}=\frac{28}{56}
=1/2
$