10-3a(a+2)=8+a

Solution for 10-3a(a+2)=8+a equation:

10-3a(a+2)=8+a

We move all terms to the left:

10-3a(a+2)-(8+a)=0

We add all the numbers together, and all the variables

-3a(a+2)-(a+8)+10=0

We multiply parentheses

-3a^2-6a-(a+8)+10=0

We get rid of parentheses

-3a^2-6a-a-8+10=0

We add all the numbers together, and all the variables

-3a^2-7a+2=0

a = -3; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·(-3)·2
Δ = 73
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{73}}{2*-3}=\frac{7-\sqrt{73}}{-6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{73}}{2*-3}=\frac{7+\sqrt{73}}{-6}
$