2x(x+4)-5=2x+3

Solution for 2x(x+4)-5=2x+3 equation:

2x(x+4)-5=2x+3

We move all terms to the left:

2x(x+4)-5-(2x+3)=0

We multiply parentheses

2x^2+8x-(2x+3)-5=0

We get rid of parentheses

2x^2+8x-2x-3-5=0

We add all the numbers together, and all the variables

2x^2+6x-8=0

a = 2; b = 6; c = -8;
Δ = b2-4ac
Δ = 62-4·2·(-8)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10}{2*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10}{2*2}=\frac{4}{4}
=1
$