2x^2=3(8-x)

Solution for 2x^2=3(8-x) equation:

2x^2=3(8-x)

We move all terms to the left:

2x^2-(3(8-x))=0

We add all the numbers together, and all the variables

2x^2-(3(-1x+8))=0


We calculate terms in parentheses: -(3(-1x+8)), so:

3(-1x+8)

We multiply parentheses

-3x+24

Back to the equation:

-(-3x+24)


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}
$