18y^2+51y-42=0

Solution for 18y^2+51y-42=0 equation:

18y^2+51y-42=0

a = 18; b = 51; c = -42;
Δ = b2-4ac
Δ = 512-4·18·(-42)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-75}{2*18}=\frac{-126}{36}
=-3+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+75}{2*18}=\frac{24}{36}
=2/3
$