(3x+1)(-2x+7)=0

Solution for (3x+1)(-2x+7)=0 equation:

(3x+1)(-2x+7)=0

We multiply parentheses ..

(-6x^2+21x-2x+7)=0

We get rid of parentheses

-6x^2+21x-2x+7=0

We add all the numbers together, and all the variables

-6x^2+19x+7=0

a = -6; b = 19; c = +7;
Δ = b2-4ac
Δ = 192-4·(-6)·7
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-23}{2*-6}=\frac{-42}{-12}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+23}{2*-6}=\frac{4}{-12}
=-1/3
$