(u+7)(u+7)=2u^2-16u+25

Solution for (u+7)(u+7)=2u^2-16u+25 equation:

(u+7)(u+7)=2u^2-16u+25

We move all terms to the left:

(u+7)(u+7)-(2u^2-16u+25)=0

We get rid of parentheses

-2u^2+(u+7)(u+7)+16u-25=0

We multiply parentheses ..

-2u^2+(+u^2+7u+7u+49)+16u-25=0

We get rid of parentheses

-2u^2+u^2+7u+7u+16u+49-25=0

We add all the numbers together, and all the variables

-1u^2+30u+24=0

a = -1; b = 30; c = +24;
Δ = b2-4ac
Δ = 302-4·(-1)·24
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{249}}{2*-1}=\frac{-30-2\sqrt{249}}{-2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{249}}{2*-1}=\frac{-30+2\sqrt{249}}{-2}
$