5x^2+100x+9=0

Solution for 5x^2+100x+9=0 equation:

5x^2+100x+9=0

a = 5; b = 100; c = +9;
Δ = b2-4ac
Δ = 1002-4·5·9
Δ = 9820
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:

$\sqrt{\Delta}=\sqrt{9820}=\sqrt{4*2455}=\sqrt{4}*\sqrt{2455}=2\sqrt{2455}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-2\sqrt{2455}}{2*5}=\frac{-100-2\sqrt{2455}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+2\sqrt{2455}}{2*5}=\frac{-100+2\sqrt{2455}}{10}
$