(7x-4)(-x+3)=0

Solution for (7x-4)(-x+3)=0 equation:

(7x-4)(-x+3)=0

We add all the numbers together, and all the variables

(7x-4)(-1x+3)=0

We multiply parentheses ..

(-7x^2+21x+4x-12)=0

We get rid of parentheses

-7x^2+21x+4x-12=0

We add all the numbers together, and all the variables

-7x^2+25x-12=0

a = -7; b = 25; c = -12;
Δ = b2-4ac
Δ = 252-4·(-7)·(-12)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-17}{2*-7}=\frac{-42}{-14}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+17}{2*-7}=\frac{-8}{-14}
=4/7
$