5x^2-45x-3=0

Solution for 5x^2-45x-3=0 equation:

5x^2-45x-3=0

a = 5; b = -45; c = -3;
Δ = b2-4ac
Δ = -452-4·5·(-3)
Δ = 2085
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{2085}}{2*5}=\frac{45-\sqrt{2085}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2085}}{2*5}=\frac{45+\sqrt{2085}}{10}
$