x^2+(x+7)(x+7)=289

Solution for x^2+(x+7)(x+7)=289 equation:

x^2+(x+7)(x+7)=289

We move all terms to the left:

x^2+(x+7)(x+7)-(289)=0

We multiply parentheses ..

x^2+(+x^2+7x+7x+49)-289=0

We get rid of parentheses

x^2+x^2+7x+7x+49-289=0

We add all the numbers together, and all the variables

2x^2+14x-240=0

a = 2; b = 14; c = -240;
Δ = b2-4ac
Δ = 142-4·2·(-240)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-46}{2*2}=\frac{-60}{4}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+46}{2*2}=\frac{32}{4}
=8
$