(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 add all the numbers together, and all the variables

(+2X^2+8X+6X+24)-84=0

We get rid of parentheses

2X^2+8X+6X+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
$