24x=1/2(36x)+16

Solution for 24x=1/2(36x)+16 equation:

24x=1/2(36x)+16

We move all terms to the left:

24x-(1/2(36x)+16)=0


Domain of the equation: 236x+16)!=0

x∈R


We get rid of parentheses

24x-1/236x-16=0

We multiply all the terms by the denominator


24x*236x-16*236x-1=0

Wy multiply elements

5664x^2-3776x-1=0

a = 5664; b = -3776; c = -1;
Δ = b2-4ac
Δ = -37762-4·5664·(-1)
Δ = 14280832
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:

$\sqrt{\Delta}=\sqrt{14280832}=\sqrt{64*223138}=\sqrt{64}*\sqrt{223138}=8\sqrt{223138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3776)-8\sqrt{223138}}{2*5664}=\frac{3776-8\sqrt{223138}}{11328}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3776)+8\sqrt{223138}}{2*5664}=\frac{3776+8\sqrt{223138}}{11328}
$