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

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

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

We multiply parentheses ..

(-2x^2+7x+8x-28)=0

We get rid of parentheses

-2x^2+7x+8x-28=0

We add all the numbers together, and all the variables

-2x^2+15x-28=0

a = -2; b = 15; c = -28;
Δ = b2-4ac
Δ = 152-4·(-2)·(-28)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-1}{2*-2}=\frac{-16}{-4}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+1}{2*-2}=\frac{-14}{-4}
=3+1/2
$