a2+8a-45=7

Solution for a2+8a-45=7 equation:

a2+8a-45=7

We move all terms to the left:

a2+8a-45-(7)=0

We add all the numbers together, and all the variables

a^2+8a-52=0

a = 1; b = 8; c = -52;
Δ = b2-4ac
Δ = 82-4·1·(-52)
Δ = 272
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{17}}{2*1}=\frac{-8-4\sqrt{17}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{17}}{2*1}=\frac{-8+4\sqrt{17}}{2}
$