(2x+1)(x+2)-77=0

Solution for (2x+1)(x+2)-77=0 equation:

(2x+1)(x+2)-77=0

We multiply parentheses ..

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

We get rid of parentheses

2x^2+4x+x+2-77=0

We add all the numbers together, and all the variables

2x^2+5x-75=0

a = 2; b = 5; c = -75;
Δ = b2-4ac
Δ = 52-4·2·(-75)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-25}{2*2}=\frac{-30}{4}
=-7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+25}{2*2}=\frac{20}{4}
=5
$