75/84a+5+4=a

Solution for 75/84a+5+4=a equation:

75/84a+5+4=a

We move all terms to the left:

75/84a+5+4-(a)=0


Domain of the equation: 84a!=0

a!=0/84

a!=0

a∈R


We add all the numbers together, and all the variables

-1a+75/84a+9=0

We multiply all the terms by the denominator


-1a*84a+9*84a+75=0

Wy multiply elements

-84a^2+756a+75=0

a = -84; b = 756; c = +75;
Δ = b2-4ac
Δ = 7562-4·(-84)·75
Δ = 596736
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:

$\sqrt{\Delta}=\sqrt{596736}=\sqrt{2304*259}=\sqrt{2304}*\sqrt{259}=48\sqrt{259}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(756)-48\sqrt{259}}{2*-84}=\frac{-756-48\sqrt{259}}{-168}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(756)+48\sqrt{259}}{2*-84}=\frac{-756+48\sqrt{259}}{-168}
$