x(2x+17)=100

Solution for x(2x+17)=100 equation:

x(2x+17)=100

We move all terms to the left:

x(2x+17)-(100)=0

We multiply parentheses

2x^2+17x-100=0

a = 2; b = 17; c = -100;
Δ = b2-4ac
Δ = 172-4·2·(-100)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-33}{2*2}=\frac{-50}{4}
=-12+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+33}{2*2}=\frac{16}{4}
=4
$