1/2a+7=3/4a+9

Solution for 1/2a+7=3/4a+9 equation:

1/2a+7=3/4a+9

We move all terms to the left:

1/2a+7-(3/4a+9)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 4a+9)!=0

a∈R


We get rid of parentheses

1/2a-3/4a-9+7=0

We calculate fractions


4a/8a^2+(-6a)/8a^2-9+7=0

We add all the numbers together, and all the variables

4a/8a^2+(-6a)/8a^2-2=0

We multiply all the terms by the denominator


4a+(-6a)-2*8a^2=0

Wy multiply elements

-16a^2+4a+(-6a)=0

We get rid of parentheses

-16a^2+4a-6a=0

We add all the numbers together, and all the variables

-16a^2-2a=0

a = -16; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-16)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-16}=\frac{0}{-32}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-16}=\frac{4}{-32}
=-1/8
$