0=5h^2-h-42

Solution for 0=5h^2-h-42 equation:

0=5h^2-h-42

We move all terms to the left:

0-(5h^2-h-42)=0

We add all the numbers together, and all the variables

-(5h^2-h-42)=0

We get rid of parentheses

-5h^2+h+42=0

a = -5; b = 1; c = +42;
Δ = b2-4ac
Δ = 12-4·(-5)·42
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-29}{2*-5}=\frac{-30}{-10}
=+3
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+29}{2*-5}=\frac{28}{-10}
=-2+4/5
$