5/4a+7=7/8a+19

Solution for 5/4a+7=7/8a+19 equation:

5/4a+7=7/8a+19

We move all terms to the left:

5/4a+7-(7/8a+19)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 8a+19)!=0

a∈R


We get rid of parentheses

5/4a-7/8a-19+7=0

We calculate fractions


40a/32a^2+(-28a)/32a^2-19+7=0

We add all the numbers together, and all the variables

40a/32a^2+(-28a)/32a^2-12=0

We multiply all the terms by the denominator


40a+(-28a)-12*32a^2=0

Wy multiply elements

-384a^2+40a+(-28a)=0

We get rid of parentheses

-384a^2+40a-28a=0

We add all the numbers together, and all the variables

-384a^2+12a=0

a = -384; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-384)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-384}=\frac{-24}{-768}
=1/32
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-384}=\frac{0}{-768}
=0
$