3X2-2x+4=-4x+9

Solution for 3X2-2x+4=-4x+9 equation:

3X^2-2X+4=-4X+9

We move all terms to the left:

3X^2-2X+4-(-4X+9)=0

We get rid of parentheses

3X^2-2X+4X-9+4=0

We add all the numbers together, and all the variables

3X^2+2X-5=0

a = 3; b = 2; c = -5;
Δ = b2-4ac
Δ = 22-4·3·(-5)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8}{2*3}=\frac{-10}{6}
=-1+2/3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8}{2*3}=\frac{6}{6}
=1
$