3/8x+x=121

Solution for 3/8x+x=121 equation:

3/8x+x=121

We move all terms to the left:

3/8x+x-(121)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/8x-121=0

We multiply all the terms by the denominator


x*8x-121*8x+3=0

Wy multiply elements

8x^2-968x+3=0

a = 8; b = -968; c = +3;
Δ = b2-4ac
Δ = -9682-4·8·3
Δ = 936928
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:

$\sqrt{\Delta}=\sqrt{936928}=\sqrt{16*58558}=\sqrt{16}*\sqrt{58558}=4\sqrt{58558}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-968)-4\sqrt{58558}}{2*8}=\frac{968-4\sqrt{58558}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-968)+4\sqrt{58558}}{2*8}=\frac{968+4\sqrt{58558}}{16}
$