1/4a-8=2a+5

Solution for 1/4a-8=2a+5 equation:

1/4a-8=2a+5

We move all terms to the left:

1/4a-8-(2a+5)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We get rid of parentheses

1/4a-2a-5-8=0

We multiply all the terms by the denominator


-2a*4a-5*4a-8*4a+1=0

Wy multiply elements

-8a^2-20a-32a+1=0

We add all the numbers together, and all the variables

-8a^2-52a+1=0

a = -8; b = -52; c = +1;
Δ = b2-4ac
Δ = -522-4·(-8)·1
Δ = 2736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2736}=\sqrt{144*19}=\sqrt{144}*\sqrt{19}=12\sqrt{19}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-12\sqrt{19}}{2*-8}=\frac{52-12\sqrt{19}}{-16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+12\sqrt{19}}{2*-8}=\frac{52+12\sqrt{19}}{-16}
$