2x(x-7)=9

Solution for 2x(x-7)=9 equation:

2x(x-7)=9

We move all terms to the left:

2x(x-7)-(9)=0

We multiply parentheses

2x^2-14x-9=0

a = 2; b = -14; c = -9;
Δ = b2-4ac
Δ = -142-4·2·(-9)
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{67}}{2*2}=\frac{14-2\sqrt{67}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{67}}{2*2}=\frac{14+2\sqrt{67}}{4}
$