8(x)=1/4x+5

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

8(x)=1/4x+5

We move all terms to the left:

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


Domain of the equation: 4x+5)!=0

x∈R


We get rid of parentheses

8x-1/4x-5=0

We multiply all the terms by the denominator


8x*4x-5*4x-1=0

Wy multiply elements

32x^2-20x-1=0

a = 32; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·32·(-1)
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{33}}{2*32}=\frac{20-4\sqrt{33}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{33}}{2*32}=\frac{20+4\sqrt{33}}{64}
$