(1/4)9x-5=32(x+8)

Solution for (1/4)9x-5=32(x+8) equation:

(1/4)9x-5=32(x+8)

We move all terms to the left:

(1/4)9x-5-(32(x+8))=0


Domain of the equation: 4)9x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/4)9x-(32(x+8))-5=0

We multiply parentheses

9x^2-(32(x+8))-5=0


We calculate terms in parentheses: -(32(x+8)), so:

32(x+8)

We multiply parentheses

32x+256

Back to the equation:

-(32x+256)


We get rid of parentheses

9x^2-32x-256-5=0

We add all the numbers together, and all the variables

9x^2-32x-261=0

a = 9; b = -32; c = -261;
Δ = b2-4ac
Δ = -322-4·9·(-261)
Δ = 10420
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:

$\sqrt{\Delta}=\sqrt{10420}=\sqrt{4*2605}=\sqrt{4}*\sqrt{2605}=2\sqrt{2605}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{2605}}{2*9}=\frac{32-2\sqrt{2605}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{2605}}{2*9}=\frac{32+2\sqrt{2605}}{18}
$