3/4a-8=a-3

Solution for 3/4a-8=a-3 equation:

3/4a-8=a-3

We move all terms to the left:

3/4a-8-(a-3)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We get rid of parentheses

3/4a-a+3-8=0

We multiply all the terms by the denominator


-a*4a+3*4a-8*4a+3=0

Wy multiply elements

-4a^2+12a-32a+3=0

We add all the numbers together, and all the variables

-4a^2-20a+3=0

a = -4; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·(-4)·3
Δ = 448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{7}}{2*-4}=\frac{20-8\sqrt{7}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{7}}{2*-4}=\frac{20+8\sqrt{7}}{-8}
$