4x^2+77=36x

Solution for 4x^2+77=36x equation:

4x^2+77=36x

We move all terms to the left:

4x^2+77-(36x)=0

a = 4; b = -36; c = +77;
Δ = b2-4ac
Δ = -362-4·4·77
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-8}{2*4}=\frac{28}{8}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+8}{2*4}=\frac{44}{8}
=5+1/2
$