(2x+4)(x+3)=100

Solution for (2x+4)(x+3)=100 equation:

(2x+4)(x+3)=100

We move all terms to the left:

(2x+4)(x+3)-(100)=0

We multiply parentheses ..

(+2x^2+6x+4x+12)-100=0

We get rid of parentheses

2x^2+6x+4x+12-100=0

We add all the numbers together, and all the variables

2x^2+10x-88=0

a = 2; b = 10; c = -88;
Δ = b2-4ac
Δ = 102-4·2·(-88)
Δ = 804
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{201}}{2*2}=\frac{-10-2\sqrt{201}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{201}}{2*2}=\frac{-10+2\sqrt{201}}{4}
$