6x=1/2x+63.5

Solution for 6x=1/2x+63.5 equation:

6x=1/2x+63.5

We move all terms to the left:

6x-(1/2x+63.5)=0


Domain of the equation: 2x+63.5)!=0

x∈R


We get rid of parentheses

6x-1/2x-63.5=0

We multiply all the terms by the denominator


6x*2x-(63.5)*2x-1=0

We multiply parentheses

6x*2x-127x-1=0

Wy multiply elements

12x^2-127x-1=0

a = 12; b = -127; c = -1;
Δ = b2-4ac
Δ = -1272-4·12·(-1)
Δ = 16177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-127)-\sqrt{16177}}{2*12}=\frac{127-\sqrt{16177}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-127)+\sqrt{16177}}{2*12}=\frac{127+\sqrt{16177}}{24}
$