4x^2+3x+1=77

Solution for 4x^2+3x+1=77 equation:

4x^2+3x+1=77

We move all terms to the left:

4x^2+3x+1-(77)=0

We add all the numbers together, and all the variables

4x^2+3x-76=0

a = 4; b = 3; c = -76;
Δ = b2-4ac
Δ = 32-4·4·(-76)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-35}{2*4}=\frac{-38}{8}
=-4+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+35}{2*4}=\frac{32}{8}
=4
$