(U+6)^2=2u^2+16u+15

Solution for (U+6)^2=2u^2+16u+15 equation:

(+6)^2=2U^2+16U+15

We move all terms to the left:

(+6)^2-(2U^2+16U+15)=0

We add all the numbers together, and all the variables

-(2U^2+16U+15)+6^2=0

We add all the numbers together, and all the variables

-(2U^2+16U+15)+36=0

We get rid of parentheses

-2U^2-16U-15+36=0

We add all the numbers together, and all the variables

-2U^2-16U+21=0

a = -2; b = -16; c = +21;
Δ = b2-4ac
Δ = -162-4·(-2)·21
Δ = 424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{106}}{2*-2}=\frac{16-2\sqrt{106}}{-4}
$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{106}}{2*-2}=\frac{16+2\sqrt{106}}{-4}
$