(9y-15)(-2/3)=34

Solution for (9y-15)(-2/3)=34 equation:

(9y-15)(-2/3)=34

We move all terms to the left:

(9y-15)(-2/3)-(34)=0

We multiply parentheses ..

(-18y^2-15*-2/3)-34=0

We multiply all the terms by the denominator


(-18y^2-15*-2-34*3)=0

We get rid of parentheses

-18y^2-2-15*-34*3=0

We add all the numbers together, and all the variables

-18y^2+1528=0

a = -18; b = 0; c = +1528;
Δ = b2-4ac
Δ = 02-4·(-18)·1528
Δ = 110016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{110016}=\sqrt{576*191}=\sqrt{576}*\sqrt{191}=24\sqrt{191}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{191}}{2*-18}=\frac{0-24\sqrt{191}}{-36}
=-\frac{24\sqrt{191}}{-36}
=-\frac{2\sqrt{191}}{-3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{191}}{2*-18}=\frac{0+24\sqrt{191}}{-36}
=\frac{24\sqrt{191}}{-36}
=\frac{2\sqrt{191}}{-3}
$