((x-4)(x+3))/2=39

Solution for ((x-4)(x+3))/2=39 equation:

((x-4)(x+3))/2=39

We move all terms to the left:

((x-4)(x+3))/2-(39)=0

We multiply parentheses ..

((+x^2+3x-4x-12))/2-39=0

We multiply all the terms by the denominator


((+x^2+3x-4x-12))-39*2=0


We calculate terms in parentheses: +((+x^2+3x-4x-12)), so:

(+x^2+3x-4x-12)

We get rid of parentheses

x^2+3x-4x-12

We add all the numbers together, and all the variables

x^2-1x-12

Back to the equation:

+(x^2-1x-12)


We add all the numbers together, and all the variables

(x^2-1x-12)-78=0

We get rid of parentheses

x^2-1x-12-78=0

We add all the numbers together, and all the variables

x^2-1x-90=0

a = 1; b = -1; c = -90;
Δ = b2-4ac
Δ = -12-4·1·(-90)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-19}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+19}{2*1}=\frac{20}{2}
=10
$