12x^2-12x-45=0

Solution for 12x^2-12x-45=0 equation:

12x^2-12x-45=0

a = 12; b = -12; c = -45;
Δ = b2-4ac
Δ = -122-4·12·(-45)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-48}{2*12}=\frac{-36}{24}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+48}{2*12}=\frac{60}{24}
=2+1/2
$