433.5=(3y+6)(3y-3.5)

Solution for 433.5=(3y+6)(3y-3.5) equation:

433.5=(3y+6)(3y-3.5)

We move all terms to the left:

433.5-((3y+6)(3y-3.5))=0

We multiply parentheses ..

-((+9y^2-10.5y+18y-21))+433.5=0


We calculate terms in parentheses: -((+9y^2-10.5y+18y-21)), so:

(+9y^2-10.5y+18y-21)

We get rid of parentheses

9y^2-10.5y+18y-21

We add all the numbers together, and all the variables

9y^2+7.5y-21

Back to the equation:

-(9y^2+7.5y-21)


We get rid of parentheses

-9y^2-7.5y+21+433.5=0

We add all the numbers together, and all the variables

-9y^2-7.5y+454.5=0

a = -9; b = -7.5; c = +454.5;
Δ = b2-4ac
Δ = -7.52-4·(-9)·454.5
Δ = 16418.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7.5)-\sqrt{16418.25}}{2*-9}=\frac{7.5-\sqrt{16418.25}}{-18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.5)+\sqrt{16418.25}}{2*-9}=\frac{7.5+\sqrt{16418.25}}{-18}
$