3x^2-8x-23=-4x-9

Solution for 3x^2-8x-23=-4x-9 equation:

3x^2-8x-23=-4x-9

We move all terms to the left:

3x^2-8x-23-(-4x-9)=0

We get rid of parentheses

3x^2-8x+4x+9-23=0

We add all the numbers together, and all the variables

3x^2-4x-14=0

a = 3; b = -4; c = -14;
Δ = b2-4ac
Δ = -42-4·3·(-14)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{46}}{2*3}=\frac{4-2\sqrt{46}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{46}}{2*3}=\frac{4+2\sqrt{46}}{6}
$