4x2-4x-5=2x(x+3)-1

Solution for 4x2-4x-5=2x(x+3)-1 equation:

4x^2-4x-5=2x(x+3)-1

We move all terms to the left:

4x^2-4x-5-(2x(x+3)-1)=0


We calculate terms in parentheses: -(2x(x+3)-1), so:

2x(x+3)-1

We multiply parentheses

2x^2+6x-1

Back to the equation:

-(2x^2+6x-1)


We get rid of parentheses

4x^2-2x^2-4x-6x+1-5=0

We add all the numbers together, and all the variables

2x^2-10x-4=0

a = 2; b = -10; c = -4;
Δ = b2-4ac
Δ = -102-4·2·(-4)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{33}}{2*2}=\frac{10-2\sqrt{33}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{33}}{2*2}=\frac{10+2\sqrt{33}}{4}
$