x^2+8x+15=43^2

Solution for x^2+8x+15=43^2 equation:

x^2+8x+15=43^2

We move all terms to the left:

x^2+8x+15-(43^2)=0

We add all the numbers together, and all the variables

x^2+8x-1834=0

a = 1; b = 8; c = -1834;
Δ = b2-4ac
Δ = 82-4·1·(-1834)
Δ = 7400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7400}=\sqrt{100*74}=\sqrt{100}*\sqrt{74}=10\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-10\sqrt{74}}{2*1}=\frac{-8-10\sqrt{74}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+10\sqrt{74}}{2*1}=\frac{-8+10\sqrt{74}}{2}
$