.5x(x+3)=77

Solution for .5x(x+3)=77 equation:

.5x(x+3)=77

We move all terms to the left:

.5x(x+3)-(77)=0

We multiply parentheses

x^2+3x-77=0

a = 1; b = 3; c = -77;
Δ = b2-4ac
Δ = 32-4·1·(-77)
Δ = 317
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{317}}{2*1}=\frac{-3-\sqrt{317}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{317}}{2*1}=\frac{-3+\sqrt{317}}{2}
$