8y2-9=-34y

Solution for 8y2-9=-34y equation:

8y^2-9=-34y

We move all terms to the left:

8y^2-9-(-34y)=0

We get rid of parentheses

8y^2+34y-9=0

a = 8; b = 34; c = -9;
Δ = b2-4ac
Δ = 342-4·8·(-9)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-38}{2*8}=\frac{-72}{16}
=-4+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+38}{2*8}=\frac{4}{16}
=1/4
$