5x^2-45x-30=0

Solution for 5x^2-45x-30=0 equation:

5x^2-45x-30=0

a = 5; b = -45; c = -30;
Δ = b2-4ac
Δ = -452-4·5·(-30)
Δ = 2625
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:

$\sqrt{\Delta}=\sqrt{2625}=\sqrt{25*105}=\sqrt{25}*\sqrt{105}=5\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-5\sqrt{105}}{2*5}=\frac{45-5\sqrt{105}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+5\sqrt{105}}{2*5}=\frac{45+5\sqrt{105}}{10}
$