(2x+1)(x-7)+22=0

Solution for (2x+1)(x-7)+22=0 equation:

(2x+1)(x-7)+22=0

We multiply parentheses ..

(+2x^2-14x+x-7)+22=0

We get rid of parentheses

2x^2-14x+x-7+22=0

We add all the numbers together, and all the variables

2x^2-13x+15=0

a = 2; b = -13; c = +15;
Δ = b2-4ac
Δ = -132-4·2·15
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-7}{2*2}=\frac{6}{4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+7}{2*2}=\frac{20}{4}
=5
$