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

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

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

We move all terms to the left:

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


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 2a+3)!=0

a∈R


We get rid of parentheses

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

We calculate fractions


6a/8a^2+(-4a)/8a^2-3-7=0

We add all the numbers together, and all the variables

6a/8a^2+(-4a)/8a^2-10=0

We multiply all the terms by the denominator


6a+(-4a)-10*8a^2=0

Wy multiply elements

-80a^2+6a+(-4a)=0

We get rid of parentheses

-80a^2+6a-4a=0

We add all the numbers together, and all the variables

-80a^2+2a=0

a = -80; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-80)·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*-80}=\frac{-4}{-160}
=1/40
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-80}=\frac{0}{-160}
=0
$