14-3x2=2(3x-5)

Solution for 14-3x2=2(3x-5) equation:

14-3x^2=2(3x-5)

We move all terms to the left:

14-3x^2-(2(3x-5))=0


We calculate terms in parentheses: -(2(3x-5)), so:

2(3x-5)

We multiply parentheses

6x-10

Back to the equation:

-(6x-10)


We get rid of parentheses

-3x^2-6x+10+14=0

We add all the numbers together, and all the variables

-3x^2-6x+24=0

a = -3; b = -6; c = +24;
Δ = b2-4ac
Δ = -62-4·(-3)·24
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*-3}=\frac{-12}{-6}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*-3}=\frac{24}{-6}
=-4
$