12x^2-8x-28+21=0

Solution for 12x^2-8x-28+21=0 equation:

12x^2-8x-28+21=0

We add all the numbers together, and all the variables

12x^2-8x-7=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
$