30=3/8x+x

Solution for 30=3/8x+x equation:

30=3/8x+x

We move all terms to the left:

30-(3/8x+x)=0


Domain of the equation: 8x+x)!=0

x∈R


We add all the numbers together, and all the variables

-(+x+3/8x)+30=0

We get rid of parentheses

-x-3/8x+30=0

We multiply all the terms by the denominator


-x*8x+30*8x-3=0

Wy multiply elements

-8x^2+240x-3=0

a = -8; b = 240; c = -3;
Δ = b2-4ac
Δ = 2402-4·(-8)·(-3)
Δ = 57504
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:

$\sqrt{\Delta}=\sqrt{57504}=\sqrt{16*3594}=\sqrt{16}*\sqrt{3594}=4\sqrt{3594}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-4\sqrt{3594}}{2*-8}=\frac{-240-4\sqrt{3594}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+4\sqrt{3594}}{2*-8}=\frac{-240+4\sqrt{3594}}{-16}
$