6x+8(1/2)x=30

Solution for 6x+8(1/2)x=30 equation:

6x+8(1/2)x=30

We move all terms to the left:

6x+8(1/2)x-(30)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x+8(+1/2)x-30=0

We multiply parentheses

8x^2+6x-30=0

a = 8; b = 6; c = -30;
Δ = b2-4ac
Δ = 62-4·8·(-30)
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{249}}{2*8}=\frac{-6-2\sqrt{249}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{249}}{2*8}=\frac{-6+2\sqrt{249}}{16}
$