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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

(x-1)(x+4)-8=0

We multiply parentheses ..

(+x^2+4x-1x-4)-8=0

We get rid of parentheses

x^2+4x-1x-4-8=0

We add all the numbers together, and all the variables

x^2+3x-12=0

a = 1; b = 3; c = -12;
Δ = b2-4ac
Δ = 32-4·1·(-12)
Δ = 57
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{-(3)-\sqrt{57}}{2*1}=\frac{-3-\sqrt{57}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*1}=\frac{-3+\sqrt{57}}{2}
$