Y=2x(3x-7)

Solution for Y=2x(3x-7) equation:

=2Y(3Y-7)

We move all terms to the left:

-(2Y(3Y-7))=0


We calculate terms in parentheses: -(2Y(3Y-7)), so:

2Y(3Y-7)

We multiply parentheses

6Y^2-14Y

Back to the equation:

-(6Y^2-14Y)


We get rid of parentheses

-6Y^2+14Y=0

a = -6; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-6)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-6}=\frac{-28}{-12}
=2+1/3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-6}=\frac{0}{-12}
=0
$