51/2a+17=5a+12

Solution for 51/2a+17=5a+12 equation:

51/2a+17=5a+12

We move all terms to the left:

51/2a+17-(5a+12)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We get rid of parentheses

51/2a-5a-12+17=0

We multiply all the terms by the denominator


-5a*2a-12*2a+17*2a+51=0

Wy multiply elements

-10a^2-24a+34a+51=0

We add all the numbers together, and all the variables

-10a^2+10a+51=0

a = -10; b = 10; c = +51;
Δ = b2-4ac
Δ = 102-4·(-10)·51
Δ = 2140
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:

$\sqrt{\Delta}=\sqrt{2140}=\sqrt{4*535}=\sqrt{4}*\sqrt{535}=2\sqrt{535}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{535}}{2*-10}=\frac{-10-2\sqrt{535}}{-20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{535}}{2*-10}=\frac{-10+2\sqrt{535}}{-20}
$