6x^2-12+20x=0

Solution for 6x^2-12+20x=0 equation:

6x^2-12+20x=0

a = 6; b = 20; c = -12;
Δ = b2-4ac
Δ = 202-4·6·(-12)
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{43}}{2*6}=\frac{-20-4\sqrt{43}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{43}}{2*6}=\frac{-20+4\sqrt{43}}{12}
$