16-2a(a-4)=a-30

Solution for 16-2a(a-4)=a-30 equation:

16-2a(a-4)=a-30

We move all terms to the left:

16-2a(a-4)-(a-30)=0

We multiply parentheses

-2a^2+8a-(a-30)+16=0

We get rid of parentheses

-2a^2+8a-a+30+16=0

We add all the numbers together, and all the variables

-2a^2+7a+46=0

a = -2; b = 7; c = +46;
Δ = b2-4ac
Δ = 72-4·(-2)·46
Δ = 417
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{417}}{2*-2}=\frac{-7-\sqrt{417}}{-4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{417}}{2*-2}=\frac{-7+\sqrt{417}}{-4}
$