3x^2+5x+9=-5x+4

Solution for 3x^2+5x+9=-5x+4 equation:

3x^2+5x+9=-5x+4

We move all terms to the left:

3x^2+5x+9-(-5x+4)=0

We get rid of parentheses

3x^2+5x+5x-4+9=0

We add all the numbers together, and all the variables

3x^2+10x+5=0

a = 3; b = 10; c = +5;
Δ = b2-4ac
Δ = 102-4·3·5
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{10}}{2*3}=\frac{-10-2\sqrt{10}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{10}}{2*3}=\frac{-10+2\sqrt{10}}{6}
$