1/2a+12=2a+5

Solution for 1/2a+12=2a+5 equation:

1/2a+12=2a+5

We move all terms to the left:

1/2a+12-(2a+5)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We get rid of parentheses

1/2a-2a-5+12=0

We multiply all the terms by the denominator


-2a*2a-5*2a+12*2a+1=0

Wy multiply elements

-4a^2-10a+24a+1=0

We add all the numbers together, and all the variables

-4a^2+14a+1=0

a = -4; b = 14; c = +1;
Δ = b2-4ac
Δ = 142-4·(-4)·1
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{53}}{2*-4}=\frac{-14-2\sqrt{53}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{53}}{2*-4}=\frac{-14+2\sqrt{53}}{-8}
$