3x+3/8x=5

Solution for 3x+3/8x=5 equation:

3x+3/8x=5

We move all terms to the left:

3x+3/8x-(5)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We multiply all the terms by the denominator


3x*8x-5*8x+3=0

Wy multiply elements

24x^2-40x+3=0

a = 24; b = -40; c = +3;
Δ = b2-4ac
Δ = -402-4·24·3
Δ = 1312
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:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{82}}{2*24}=\frac{40-4\sqrt{82}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{82}}{2*24}=\frac{40+4\sqrt{82}}{48}
$