50-5a=1/2a

Solution for 50-5a=1/2a equation:

50-5a=1/2a

We move all terms to the left:

50-5a-(1/2a)=0


Domain of the equation: 2a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

-5a-(+1/2a)+50=0

We get rid of parentheses

-5a-1/2a+50=0

We multiply all the terms by the denominator


-5a*2a+50*2a-1=0

Wy multiply elements

-10a^2+100a-1=0

a = -10; b = 100; c = -1;
Δ = b2-4ac
Δ = 1002-4·(-10)·(-1)
Δ = 9960
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:

$\sqrt{\Delta}=\sqrt{9960}=\sqrt{4*2490}=\sqrt{4}*\sqrt{2490}=2\sqrt{2490}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-2\sqrt{2490}}{2*-10}=\frac{-100-2\sqrt{2490}}{-20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+2\sqrt{2490}}{2*-10}=\frac{-100+2\sqrt{2490}}{-20}
$