77.1=55x-4.91x^2

Solution for 77.1=55x-4.91x^2 equation:

77.1=55x-4.91x^2

We move all terms to the left:

77.1-(55x-4.91x^2)=0

We get rid of parentheses

4.91x^2-55x+77.1=0

a = 4.91; b = -55; c = +77.1;
Δ = b2-4ac
Δ = -552-4·4.91·77.1
Δ = 1510.756
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{-(-55)-\sqrt{1510.756}}{2*4.91}=\frac{55-\sqrt{1510.756}}{9.82}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{1510.756}}{2*4.91}=\frac{55+\sqrt{1510.756}}{9.82}
$