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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

4x^2+4x-5x-5+3=0

We add all the numbers together, and all the variables

4x^2-1x-2=0

a = 4; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·4·(-2)
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{33}}{2*4}=\frac{1-\sqrt{33}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{33}}{2*4}=\frac{1+\sqrt{33}}{8}
$