69x^2-90x-450=0

Solution for 69x^2-90x-450=0 equation:

69x^2-90x-450=0

a = 69; b = -90; c = -450;
Δ = b2-4ac
Δ = -902-4·69·(-450)
Δ = 132300
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:

$\sqrt{\Delta}=\sqrt{132300}=\sqrt{44100*3}=\sqrt{44100}*\sqrt{3}=210\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-210\sqrt{3}}{2*69}=\frac{90-210\sqrt{3}}{138}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+210\sqrt{3}}{2*69}=\frac{90+210\sqrt{3}}{138}
$