(X+6)2=2x2+13x+16

Solution for (X+6)2=2x2+13x+16 equation:

(X+6)2=2X^2+13X+16

We move all terms to the left:

(X+6)2-(2X^2+13X+16)=0

We multiply parentheses

2X-(2X^2+13X+16)+12=0

We get rid of parentheses

-2X^2+2X-13X-16+12=0

We add all the numbers together, and all the variables

-2X^2-11X-4=0

a = -2; b = -11; c = -4;
Δ = b2-4ac
Δ = -112-4·(-2)·(-4)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{89}}{2*-2}=\frac{11-\sqrt{89}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{89}}{2*-2}=\frac{11+\sqrt{89}}{-4}
$