4x+3/8x-7=0

Solution for 4x+3/8x-7=0 equation:

4x+3/8x-7=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We multiply all the terms by the denominator


4x*8x-7*8x+3=0

Wy multiply elements

32x^2-56x+3=0

a = 32; b = -56; c = +3;
Δ = b2-4ac
Δ = -562-4·32·3
Δ = 2752
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:

$\sqrt{\Delta}=\sqrt{2752}=\sqrt{64*43}=\sqrt{64}*\sqrt{43}=8\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{43}}{2*32}=\frac{56-8\sqrt{43}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{43}}{2*32}=\frac{56+8\sqrt{43}}{64}
$