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

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

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

We move all terms to the left:

-1/4a-4-(7/2a-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

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

We calculate fractions


(-2a)/8a^2+(-28a)/8a^2+3-4=0

We add all the numbers together, and all the variables

(-2a)/8a^2+(-28a)/8a^2-1=0

We multiply all the terms by the denominator


(-2a)+(-28a)-1*8a^2=0

Wy multiply elements

-8a^2+(-2a)+(-28a)=0

We get rid of parentheses

-8a^2-2a-28a=0

We add all the numbers together, and all the variables

-8a^2-30a=0

a = -8; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·(-8)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*-8}=\frac{0}{-16}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*-8}=\frac{60}{-16}
=-3+3/4
$