8x=1/2x+30

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

8x=1/2x+30

We move all terms to the left:

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


Domain of the equation: 2x+30)!=0

x∈R


We get rid of parentheses

8x-1/2x-30=0

We multiply all the terms by the denominator


8x*2x-30*2x-1=0

Wy multiply elements

16x^2-60x-1=0

a = 16; b = -60; c = -1;
Δ = b2-4ac
Δ = -602-4·16·(-1)
Δ = 3664
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:

$\sqrt{\Delta}=\sqrt{3664}=\sqrt{16*229}=\sqrt{16}*\sqrt{229}=4\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{229}}{2*16}=\frac{60-4\sqrt{229}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{229}}{2*16}=\frac{60+4\sqrt{229}}{32}
$