((x+3)(2x+8))/(2)=42

Solution for ((x+3)(2x+8))/(2)=42 equation:

((x+3)(2x+8))/(2)=42

We move all terms to the left:

((x+3)(2x+8))/(2)-(42)=0

We multiply parentheses ..

((+2x^2+8x+6x+24))/2-42=0

We multiply all the terms by the denominator


((+2x^2+8x+6x+24))-42*2=0


We calculate terms in parentheses: +((+2x^2+8x+6x+24)), so:

(+2x^2+8x+6x+24)

We get rid of parentheses

2x^2+8x+6x+24

We add all the numbers together, and all the variables

2x^2+14x+24

Back to the equation:

+(2x^2+14x+24)


We add all the numbers together, and all the variables

(2x^2+14x+24)-84=0

We get rid of parentheses

2x^2+14x+24-84=0

We add all the numbers together, and all the variables

2x^2+14x-60=0

a = 2; b = 14; c = -60;
Δ = b2-4ac
Δ = 142-4·2·(-60)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-26}{2*2}=\frac{-40}{4}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+26}{2*2}=\frac{12}{4}
=3
$