6x-20=-3x2

Solution for 6x-20=-3x2 equation:

6x-20=-3x^2

We move all terms to the left:

6x-20-(-3x^2)=0

We get rid of parentheses

3x^2+6x-20=0

a = 3; b = 6; c = -20;
Δ = b2-4ac
Δ = 62-4·3·(-20)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{69}}{2*3}=\frac{-6-2\sqrt{69}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{69}}{2*3}=\frac{-6+2\sqrt{69}}{6}
$