(7x-2)(8-3x)=0

Solution for (7x-2)(8-3x)=0 equation:

(7x-2)(8-3x)=0

We add all the numbers together, and all the variables

(7x-2)(-3x+8)=0

We multiply parentheses ..

(-21x^2+56x+6x-16)=0

We get rid of parentheses

-21x^2+56x+6x-16=0

We add all the numbers together, and all the variables

-21x^2+62x-16=0

a = -21; b = 62; c = -16;
Δ = b2-4ac
Δ = 622-4·(-21)·(-16)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-50}{2*-21}=\frac{-112}{-42}
=2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+50}{2*-21}=\frac{-12}{-42}
=2/7
$