8a^2+45a-9=0

Solution for 8a^2+45a-9=0 equation:

8a^2+45a-9=0

a = 8; b = 45; c = -9;
Δ = b2-4ac
Δ = 452-4·8·(-9)
Δ = 2313
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:

$\sqrt{\Delta}=\sqrt{2313}=\sqrt{9*257}=\sqrt{9}*\sqrt{257}=3\sqrt{257}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{257}}{2*8}=\frac{-45-3\sqrt{257}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{257}}{2*8}=\frac{-45+3\sqrt{257}}{16}
$