8=3/4a+13-a+4

Solution for 8=3/4a+13-a+4 equation:

8=3/4a+13-a+4

We move all terms to the left:

8-(3/4a+13-a+4)=0


Domain of the equation: 4a+13-a+4)!=0

We move all terms containing a to the left, all other terms to the right

4a-a+4)!=-13

a∈R


We add all the numbers together, and all the variables

-(-1a+3/4a+17)+8=0

We get rid of parentheses

1a-3/4a-17+8=0

We multiply all the terms by the denominator


1a*4a-17*4a+8*4a-3=0

Wy multiply elements

4a^2-68a+32a-3=0

We add all the numbers together, and all the variables

4a^2-36a-3=0

a = 4; b = -36; c = -3;
Δ = b2-4ac
Δ = -362-4·4·(-3)
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-8\sqrt{21}}{2*4}=\frac{36-8\sqrt{21}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+8\sqrt{21}}{2*4}=\frac{36+8\sqrt{21}}{8}
$