(x-7)(2x+17)=0

Solution for (x-7)(2x+17)=0 equation:

(x-7)(2x+17)=0

We multiply parentheses ..

(+2x^2+17x-14x-119)=0

We get rid of parentheses

2x^2+17x-14x-119=0

We add all the numbers together, and all the variables

2x^2+3x-119=0

a = 2; b = 3; c = -119;
Δ = b2-4ac
Δ = 32-4·2·(-119)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-31}{2*2}=\frac{-34}{4}
=-8+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+31}{2*2}=\frac{28}{4}
=7
$