6x^2-15x-75=0

Solution for 6x^2-15x-75=0 equation:

6x^2-15x-75=0

a = 6; b = -15; c = -75;
Δ = b2-4ac
Δ = -152-4·6·(-75)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-45}{2*6}=\frac{-30}{12}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+45}{2*6}=\frac{60}{12}
=5
$