24x^2=9-30x

Solution for 24x^2=9-30x equation:

24x^2=9-30x

We move all terms to the left:

24x^2-(9-30x)=0

We add all the numbers together, and all the variables

24x^2-(-30x+9)=0

We get rid of parentheses

24x^2+30x-9=0

a = 24; b = 30; c = -9;
Δ = b2-4ac
Δ = 302-4·24·(-9)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-42}{2*24}=\frac{-72}{48}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+42}{2*24}=\frac{12}{48}
=1/4
$