a^2+7a-45=7

Solution for a^2+7a-45=7 equation:

a^2+7a-45=7

We move all terms to the left:

a^2+7a-45-(7)=0

We add all the numbers together, and all the variables

a^2+7a-52=0

a = 1; b = 7; c = -52;
Δ = b2-4ac
Δ = 72-4·1·(-52)
Δ = 257
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{257}}{2*1}=\frac{-7-\sqrt{257}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{257}}{2*1}=\frac{-7+\sqrt{257}}{2}
$