3x^2=-9x^2-12x+22

Solution for 3x^2=-9x^2-12x+22 equation:

3x^2=-9x^2-12x+22

We move all terms to the left:

3x^2-(-9x^2-12x+22)=0

We get rid of parentheses

3x^2+9x^2+12x-22=0

We add all the numbers together, and all the variables

12x^2+12x-22=0

a = 12; b = 12; c = -22;
Δ = b2-4ac
Δ = 122-4·12·(-22)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-20\sqrt{3}}{2*12}=\frac{-12-20\sqrt{3}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+20\sqrt{3}}{2*12}=\frac{-12+20\sqrt{3}}{24}
$