Y=x(3x-7)

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

=Y(3Y-7)

We move all terms to the left:

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


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

Y(3Y-7)

We multiply parentheses

3Y^2-7Y

Back to the equation:

-(3Y^2-7Y)


We get rid of parentheses

-3Y^2+7Y=0

a = -3; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-3)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-3}=\frac{-14}{-6}
=2+1/3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-3}=\frac{0}{-6}
=0
$