4x^2+12x+9=-5x+24

Solution for 4x^2+12x+9=-5x+24 equation:

4x^2+12x+9=-5x+24

We move all terms to the left:

4x^2+12x+9-(-5x+24)=0

We get rid of parentheses

4x^2+12x+5x-24+9=0

We add all the numbers together, and all the variables

4x^2+17x-15=0

a = 4; b = 17; c = -15;
Δ = b2-4ac
Δ = 172-4·4·(-15)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-23}{2*4}=\frac{-40}{8}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+23}{2*4}=\frac{6}{8}
=3/4
$