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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

x(x+4)-(2x+8)=0

We multiply parentheses

x^2+4x-(2x+8)=0

We get rid of parentheses

x^2+4x-2x-8=0

We add all the numbers together, and all the variables

x^2+2x-8=0

a = 1; b = 2; c = -8;
Δ = b2-4ac
Δ = 22-4·1·(-8)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*1}=\frac{4}{2}
=2
$