63/4a=1/2a+1

Solution for 63/4a=1/2a+1 equation:

63/4a=1/2a+1

We move all terms to the left:

63/4a-(1/2a+1)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 2a+1)!=0

a∈R


We get rid of parentheses

63/4a-1/2a-1=0

We calculate fractions


126a/8a^2+(-4a)/8a^2-1=0

We multiply all the terms by the denominator


126a+(-4a)-1*8a^2=0

Wy multiply elements

-8a^2+126a+(-4a)=0

We get rid of parentheses

-8a^2+126a-4a=0

We add all the numbers together, and all the variables

-8a^2+122a=0

a = -8; b = 122; c = 0;
Δ = b2-4ac
Δ = 1222-4·(-8)·0
Δ = 14884
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14884}=122$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(122)-122}{2*-8}=\frac{-244}{-16}
=15+1/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(122)+122}{2*-8}=\frac{0}{-16}
=0
$