24-2x(x=3)

Solution for 24-2x(x=3) equation:

24-2x(x=3)

We move all terms to the left:

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

We multiply parentheses

-2x^2+6x+24=0

a = -2; b = 6; c = +24;
Δ = b2-4ac
Δ = 62-4·(-2)·24
Δ = 228
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{57}}{2*-2}=\frac{-6-2\sqrt{57}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{57}}{2*-2}=\frac{-6+2\sqrt{57}}{-4}
$