2x(x+7)=17

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

2x(x+7)=17

We move all terms to the left:

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

We multiply parentheses

2x^2+14x-17=0

a = 2; b = 14; c = -17;
Δ = b2-4ac
Δ = 142-4·2·(-17)
Δ = 332
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:

$\sqrt{\Delta}=\sqrt{332}=\sqrt{4*83}=\sqrt{4}*\sqrt{83}=2\sqrt{83}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{83}}{2*2}=\frac{-14-2\sqrt{83}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{83}}{2*2}=\frac{-14+2\sqrt{83}}{4}
$