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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

(x+3)

We get rid of parentheses

x+3

Back to the equation:

-(x+3)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-5x-3=0

a = 1; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·1·(-3)
Δ = 37
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{-(-5)-\sqrt{37}}{2*1}=\frac{5-\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{37}}{2*1}=\frac{5+\sqrt{37}}{2}
$