1/7a+3/4=9/8;a=

Solution for 1/7a+3/4=9/8;a= equation:

1/7a+3/4=9/8a=

We move all terms to the left:

1/7a+3/4-(9/8a)=0


Domain of the equation: 7a!=0

a!=0/7

a!=0

a∈R



Domain of the equation: 8a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

1/7a-(+9/8a)+3/4=0

We get rid of parentheses

1/7a-9/8a+3/4=0

We calculate fractions


1344a^2/896a^2+128a/896a^2+(-1008a)/896a^2=0

We multiply all the terms by the denominator


1344a^2+128a+(-1008a)=0

We get rid of parentheses

1344a^2+128a-1008a=0

We add all the numbers together, and all the variables

1344a^2-880a=0

a = 1344; b = -880; c = 0;
Δ = b2-4ac
Δ = -8802-4·1344·0
Δ = 774400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{774400}=880$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-880)-880}{2*1344}=\frac{0}{2688}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-880)+880}{2*1344}=\frac{1760}{2688}
=55/84
$