77=0.5(h+3)h

Solution for 77=0.5(h+3)h equation:

77=0.5(h+3)h

We move all terms to the left:

77-(0.5(h+3)h)=0


We calculate terms in parentheses: -(0.5(h+3)h), so:

0.5(h+3)h

We multiply parentheses

0h^2+0h

We add all the numbers together, and all the variables

h^2+h

Back to the equation:

-(h^2+h)


We get rid of parentheses

-h^2-h+77=0

We add all the numbers together, and all the variables

-1h^2-1h+77=0

a = -1; b = -1; c = +77;
Δ = b2-4ac
Δ = -12-4·(-1)·77
Δ = 309
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{309}}{2*-1}=\frac{1-\sqrt{309}}{-2}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{309}}{2*-1}=\frac{1+\sqrt{309}}{-2}
$