10x^2-30x-38=0

Solution for 10x^2-30x-38=0 equation:

10x^2-30x-38=0

a = 10; b = -30; c = -38;
Δ = b2-4ac
Δ = -302-4·10·(-38)
Δ = 2420
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:

$\sqrt{\Delta}=\sqrt{2420}=\sqrt{484*5}=\sqrt{484}*\sqrt{5}=22\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-22\sqrt{5}}{2*10}=\frac{30-22\sqrt{5}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+22\sqrt{5}}{2*10}=\frac{30+22\sqrt{5}}{20}
$