2u^2+8u+15=(u+6)(u+6)

Solution for 2u^2+8u+15=(u+6)(u+6) equation:

2u^2+8u+15=(u+6)(u+6)

We move all terms to the left:

2u^2+8u+15-((u+6)(u+6))=0

We multiply parentheses ..

2u^2-((+u^2+6u+6u+36))+8u+15=0


We calculate terms in parentheses: -((+u^2+6u+6u+36)), so:

(+u^2+6u+6u+36)

We get rid of parentheses

u^2+6u+6u+36

We add all the numbers together, and all the variables

u^2+12u+36

Back to the equation:

-(u^2+12u+36)


We add all the numbers together, and all the variables

2u^2+8u-(u^2+12u+36)+15=0

We get rid of parentheses

2u^2-u^2+8u-12u-36+15=0

We add all the numbers together, and all the variables

u^2-4u-21=0

a = 1; b = -4; c = -21;
Δ = b2-4ac
Δ = -42-4·1·(-21)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-10}{2*1}=\frac{-6}{2}
=-3
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+10}{2*1}=\frac{14}{2}
=7
$