3x^2+7=-9x^+4

Solution for 3x^2+7=-9x^+4 equation:

3x^2+7=-9x^+4

We move all terms to the left:

3x^2+7-(-9x^+4)=0

We get rid of parentheses

3x^2+9x^-4+7=0

We add all the numbers together, and all the variables

3x^2+9x+3=0

a = 3; b = 9; c = +3;
Δ = b2-4ac
Δ = 92-4·3·3
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{5}}{2*3}=\frac{-9-3\sqrt{5}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{5}}{2*3}=\frac{-9+3\sqrt{5}}{6}
$