-5y^2+30y-42=0

Solution for -5y^2+30y-42=0 equation:

-5y^2+30y-42=0

a = -5; b = 30; c = -42;
Δ = b2-4ac
Δ = 302-4·(-5)·(-42)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{15}}{2*-5}=\frac{-30-2\sqrt{15}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{15}}{2*-5}=\frac{-30+2\sqrt{15}}{-10}
$