7-8x-12x^2=0

Solution for 7-8x-12x^2=0 equation:

7-8x-12x^2=0

a = -12; b = -8; c = +7;
Δ = b2-4ac
Δ = -82-4·(-12)·7
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-20}{2*-12}=\frac{-12}{-24}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+20}{2*-12}=\frac{28}{-24}
=-1+1/6
$