1/2x+9=4x+5

Solution for 1/2x+9=4x+5 equation:

1/2x+9=4x+5

We move all terms to the left:

1/2x+9-(4x+5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-4x-5+9=0

We multiply all the terms by the denominator


-4x*2x-5*2x+9*2x+1=0

Wy multiply elements

-8x^2-10x+18x+1=0

We add all the numbers together, and all the variables

-8x^2+8x+1=0

a = -8; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·(-8)·1
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{6}}{2*-8}=\frac{-8-4\sqrt{6}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{6}}{2*-8}=\frac{-8+4\sqrt{6}}{-16}
$