x(2x-7)-4x+14=0

Solution for x(2x-7)-4x+14=0 equation:

x(2x-7)-4x+14=0

We add all the numbers together, and all the variables

-4x+x(2x-7)+14=0

We multiply parentheses

2x^2-4x-7x+14=0

We add all the numbers together, and all the variables

2x^2-11x+14=0

a = 2; b = -11; c = +14;
Δ = b2-4ac
Δ = -112-4·2·14
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3}{2*2}=\frac{8}{4}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3}{2*2}=\frac{14}{4}
=3+1/2
$