4+10a+a^2-3(a+2)-13=0

Solution for 4+10a+a^2-3(a+2)-13=0 equation:

4+10a+a^2-3(a+2)-13=0

We add all the numbers together, and all the variables

a^2+10a-3(a+2)-9=0

We multiply parentheses

a^2+10a-3a-6-9=0

We add all the numbers together, and all the variables

a^2+7a-15=0

a = 1; b = 7; c = -15;
Δ = b2-4ac
Δ = 72-4·1·(-15)
Δ = 109
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{109}}{2*1}=\frac{-7-\sqrt{109}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{109}}{2*1}=\frac{-7+\sqrt{109}}{2}
$