30x^2-38x-3=0

Solution for 30x^2-38x-3=0 equation:

30x^2-38x-3=0

a = 30; b = -38; c = -3;
Δ = b2-4ac
Δ = -382-4·30·(-3)
Δ = 1804
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:

$\sqrt{\Delta}=\sqrt{1804}=\sqrt{4*451}=\sqrt{4}*\sqrt{451}=2\sqrt{451}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{451}}{2*30}=\frac{38-2\sqrt{451}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{451}}{2*30}=\frac{38+2\sqrt{451}}{60}
$