10a^2-20a-45=0

Solution for 10a^2-20a-45=0 equation:

10a^2-20a-45=0

a = 10; b = -20; c = -45;
Δ = b2-4ac
Δ = -202-4·10·(-45)
Δ = 2200
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:

$\sqrt{\Delta}=\sqrt{2200}=\sqrt{100*22}=\sqrt{100}*\sqrt{22}=10\sqrt{22}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10\sqrt{22}}{2*10}=\frac{20-10\sqrt{22}}{20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10\sqrt{22}}{2*10}=\frac{20+10\sqrt{22}}{20}
$