5x-2x(x-7)-6=17

Solution for 5x-2x(x-7)-6=17 equation:

5x-2x(x-7)-6=17

We move all terms to the left:

5x-2x(x-7)-6-(17)=0

We add all the numbers together, and all the variables

5x-2x(x-7)-23=0

We multiply parentheses

-2x^2+5x+14x-23=0

We add all the numbers together, and all the variables

-2x^2+19x-23=0

a = -2; b = 19; c = -23;
Δ = b2-4ac
Δ = 192-4·(-2)·(-23)
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-\sqrt{177}}{2*-2}=\frac{-19-\sqrt{177}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{177}}{2*-2}=\frac{-19+\sqrt{177}}{-4}
$