3x^2-4x+6=-9x+4

Solution for 3x^2-4x+6=-9x+4 equation:

3x^2-4x+6=-9x+4

We move all terms to the left:

3x^2-4x+6-(-9x+4)=0

We get rid of parentheses

3x^2-4x+9x-4+6=0

We add all the numbers together, and all the variables

3x^2+5x+2=0

a = 3; b = 5; c = +2;
Δ = b2-4ac
Δ = 52-4·3·2
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-1}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*3}=\frac{-4}{6}
=-2/3
$