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

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

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

We move all terms to the left:

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


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 4a-3)!=0

a∈R


We get rid of parentheses

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

We calculate fractions


(-4a)/8a^2+(-14a)/8a^2+3-4=0

We add all the numbers together, and all the variables

(-4a)/8a^2+(-14a)/8a^2-1=0

We multiply all the terms by the denominator


(-4a)+(-14a)-1*8a^2=0

Wy multiply elements

-8a^2+(-4a)+(-14a)=0

We get rid of parentheses

-8a^2-4a-14a=0

We add all the numbers together, and all the variables

-8a^2-18a=0

a = -8; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-8)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-8}=\frac{0}{-16}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-8}=\frac{36}{-16}
=-2+1/4
$