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

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

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

We move all terms to the left:

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


Domain of the equation: 1a!=0

a∈R



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

a∈R


We get rid of parentheses

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

We calculate fractions


16a/4a^2+(-7a)/4a^2+3-4=0

We add all the numbers together, and all the variables

16a/4a^2+(-7a)/4a^2-1=0

We multiply all the terms by the denominator


16a+(-7a)-1*4a^2=0

Wy multiply elements

-4a^2+16a+(-7a)=0

We get rid of parentheses

-4a^2+16a-7a=0

We add all the numbers together, and all the variables

-4a^2+9a=0

a = -4; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-4)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-4}=\frac{-18}{-8}
=2+1/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-4}=\frac{0}{-8}
=0
$