(4p-7)(p+6)=0

Solution for (4p-7)(p+6)=0 equation:

(4p-7)(p+6)=0

We multiply parentheses ..

(+4p^2+24p-7p-42)=0

We get rid of parentheses

4p^2+24p-7p-42=0

We add all the numbers together, and all the variables

4p^2+17p-42=0

a = 4; b = 17; c = -42;
Δ = b2-4ac
Δ = 172-4·4·(-42)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-31}{2*4}=\frac{-48}{8}
=-6
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+31}{2*4}=\frac{14}{8}
=1+3/4
$