24x^2=42+27x

Solution for 24x^2=42+27x equation:

24x^2=42+27x

We move all terms to the left:

24x^2-(42+27x)=0

We add all the numbers together, and all the variables

24x^2-(27x+42)=0

We get rid of parentheses

24x^2-27x-42=0

a = 24; b = -27; c = -42;
Δ = b2-4ac
Δ = -272-4·24·(-42)
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-69}{2*24}=\frac{-42}{48}
=-7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+69}{2*24}=\frac{96}{48}
=2
$