2x^2=24-3x

Solution for 2x^2=24-3x equation:

2x^2=24-3x

We move all terms to the left:

2x^2-(24-3x)=0

We add all the numbers together, and all the variables

2x^2-(-3x+24)=0

We get rid of parentheses

2x^2+3x-24=0

a = 2; b = 3; c = -24;
Δ = b2-4ac
Δ = 32-4·2·(-24)
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{201}}{2*2}=\frac{-3-\sqrt{201}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{201}}{2*2}=\frac{-3+\sqrt{201}}{4}
$