(7x+2)(20-3x)/4=0

Solution for (7x+2)(20-3x)/4=0 equation:

(7x+2)(20-3x)/4=0

We add all the numbers together, and all the variables

(7x+2)(-3x+20)/4=0

We multiply parentheses ..

(-21x^2+140x-6x+40)/4=0

We multiply all the terms by the denominator


(-21x^2+140x-6x+40)=0

We get rid of parentheses

-21x^2+140x-6x+40=0

We add all the numbers together, and all the variables

-21x^2+134x+40=0

a = -21; b = 134; c = +40;
Δ = b2-4ac
Δ = 1342-4·(-21)·40
Δ = 21316
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21316}=146$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(134)-146}{2*-21}=\frac{-280}{-42}
=6+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(134)+146}{2*-21}=\frac{12}{-42}
=-2/7
$