x+3/8,x=4

Solution for x+3/8,x=4 equation:

x+3/8.x=4

We move all terms to the left:

x+3/8.x-(4)=0


Domain of the equation: 8.x!=0

x!=0/8.

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

8x^2-32x+3=0

a = 8; b = -32; c = +3;
Δ = b2-4ac
Δ = -322-4·8·3
Δ = 928
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:

$\sqrt{\Delta}=\sqrt{928}=\sqrt{16*58}=\sqrt{16}*\sqrt{58}=4\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{58}}{2*8}=\frac{32-4\sqrt{58}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{58}}{2*8}=\frac{32+4\sqrt{58}}{16}
$