31/4a-12=3a-15

Solution for 31/4a-12=3a-15 equation:

31/4a-12=3a-15

We move all terms to the left:

31/4a-12-(3a-15)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We get rid of parentheses

31/4a-3a+15-12=0

We multiply all the terms by the denominator


-3a*4a+15*4a-12*4a+31=0

Wy multiply elements

-12a^2+60a-48a+31=0

We add all the numbers together, and all the variables

-12a^2+12a+31=0

a = -12; b = 12; c = +31;
Δ = b2-4ac
Δ = 122-4·(-12)·31
Δ = 1632
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:

$\sqrt{\Delta}=\sqrt{1632}=\sqrt{16*102}=\sqrt{16}*\sqrt{102}=4\sqrt{102}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{102}}{2*-12}=\frac{-12-4\sqrt{102}}{-24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{102}}{2*-12}=\frac{-12+4\sqrt{102}}{-24}
$