(3x^2)=24-14x

Solution for (3x^2)=24-14x equation:

(3x^2)=24-14x

We move all terms to the left:

(3x^2)-(24-14x)=0

We add all the numbers together, and all the variables

3x^2-(-14x+24)=0

We get rid of parentheses

3x^2+14x-24=0

a = 3; b = 14; c = -24;
Δ = b2-4ac
Δ = 142-4·3·(-24)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-22}{2*3}=\frac{-36}{6}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+22}{2*3}=\frac{8}{6}
=1+1/3
$