41/4a-17=4a-14

Solution for 41/4a-17=4a-14 equation:

41/4a-17=4a-14

We move all terms to the left:

41/4a-17-(4a-14)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We get rid of parentheses

41/4a-4a+14-17=0

We multiply all the terms by the denominator


-4a*4a+14*4a-17*4a+41=0

Wy multiply elements

-16a^2+56a-68a+41=0

We add all the numbers together, and all the variables

-16a^2-12a+41=0

a = -16; b = -12; c = +41;
Δ = b2-4ac
Δ = -122-4·(-16)·41
Δ = 2768
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:

$\sqrt{\Delta}=\sqrt{2768}=\sqrt{16*173}=\sqrt{16}*\sqrt{173}=4\sqrt{173}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{173}}{2*-16}=\frac{12-4\sqrt{173}}{-32}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{173}}{2*-16}=\frac{12+4\sqrt{173}}{-32}
$