5x+3/4x-7=0

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

5x+3/4x-7=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

20x^2-28x+3=0

a = 20; b = -28; c = +3;
Δ = b2-4ac
Δ = -282-4·20·3
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{34}}{2*20}=\frac{28-4\sqrt{34}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{34}}{2*20}=\frac{28+4\sqrt{34}}{40}
$