1/2x+5/8x=18

Solution for 1/2x+5/8x=18 equation:

1/2x+5/8x=18

We move all terms to the left:

1/2x+5/8x-(18)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We calculate fractions


8x/16x^2+10x/16x^2-18=0

We multiply all the terms by the denominator


8x+10x-18*16x^2=0

We add all the numbers together, and all the variables

18x-18*16x^2=0

Wy multiply elements

-288x^2+18x=0

a = -288; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-288)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-288}=\frac{-36}{-576}
=1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-288}=\frac{0}{-576}
=0
$