225x^2-150x-1=0

Solution for 225x^2-150x-1=0 equation:

225x^2-150x-1=0

a = 225; b = -150; c = -1;
Δ = b2-4ac
Δ = -1502-4·225·(-1)
Δ = 23400
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:

$\sqrt{\Delta}=\sqrt{23400}=\sqrt{900*26}=\sqrt{900}*\sqrt{26}=30\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-30\sqrt{26}}{2*225}=\frac{150-30\sqrt{26}}{450}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+30\sqrt{26}}{2*225}=\frac{150+30\sqrt{26}}{450}
$