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

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

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

We move all terms to the left:

9-1/2x-(4(x)+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 = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{2}}{2*-8}=\frac{-8-4\sqrt{2}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{2}}{2*-8}=\frac{-8+4\sqrt{2}}{-16}
$