31/2a-16=3a-10

Solution for 31/2a-16=3a-10 equation:

31/2a-16=3a-10

We move all terms to the left:

31/2a-16-(3a-10)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We get rid of parentheses

31/2a-3a+10-16=0

We multiply all the terms by the denominator


-3a*2a+10*2a-16*2a+31=0

Wy multiply elements

-6a^2+20a-32a+31=0

We add all the numbers together, and all the variables

-6a^2-12a+31=0

a = -6; b = -12; c = +31;
Δ = b2-4ac
Δ = -122-4·(-6)·31
Δ = 888
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:

$\sqrt{\Delta}=\sqrt{888}=\sqrt{4*222}=\sqrt{4}*\sqrt{222}=2\sqrt{222}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{222}}{2*-6}=\frac{12-2\sqrt{222}}{-12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{222}}{2*-6}=\frac{12+2\sqrt{222}}{-12}
$