2x(5+3x)-4(x+5)=100

Solution for 2x(5+3x)-4(x+5)=100 equation:

2x(5+3x)-4(x+5)=100

We move all terms to the left:

2x(5+3x)-4(x+5)-(100)=0

We add all the numbers together, and all the variables

2x(3x+5)-4(x+5)-100=0

We multiply parentheses

6x^2+10x-4x-20-100=0

We add all the numbers together, and all the variables

6x^2+6x-120=0

a = 6; b = 6; c = -120;
Δ = b2-4ac
Δ = 62-4·6·(-120)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-54}{2*6}=\frac{-60}{12}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+54}{2*6}=\frac{48}{12}
=4
$