38x2-10x-75=0

Solution for 38x2-10x-75=0 equation:

38x^2-10x-75=0

a = 38; b = -10; c = -75;
Δ = b2-4ac
Δ = -102-4·38·(-75)
Δ = 11500
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:

$\sqrt{\Delta}=\sqrt{11500}=\sqrt{100*115}=\sqrt{100}*\sqrt{115}=10\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{115}}{2*38}=\frac{10-10\sqrt{115}}{76}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{115}}{2*38}=\frac{10+10\sqrt{115}}{76}
$