4x(x+5)+6x+22=2x+5

Solution for 4x(x+5)+6x+22=2x+5 equation:

4x(x+5)+6x+22=2x+5

We move all terms to the left:

4x(x+5)+6x+22-(2x+5)=0

We add all the numbers together, and all the variables

6x+4x(x+5)-(2x+5)+22=0

We multiply parentheses

4x^2+6x+20x-(2x+5)+22=0

We get rid of parentheses

4x^2+6x+20x-2x-5+22=0

We add all the numbers together, and all the variables

4x^2+24x+17=0

a = 4; b = 24; c = +17;
Δ = b2-4ac
Δ = 242-4·4·17
Δ = 304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{19}}{2*4}=\frac{-24-4\sqrt{19}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{19}}{2*4}=\frac{-24+4\sqrt{19}}{8}
$