(5d-12)(-7=3d)

Solution for (5d-12)(-7=3d) equation:

(5d-12)(-7=3d)

We move all terms to the left:

(5d-12)(-7-(3d))=0

We add all the numbers together, and all the variables

(5d-12)(-3d-7)=0

We multiply parentheses ..

(-15d^2-35d+36d+84)=0

We get rid of parentheses

-15d^2-35d+36d+84=0

We add all the numbers together, and all the variables

-15d^2+d+84=0

a = -15; b = 1; c = +84;
Δ = b2-4ac
Δ = 12-4·(-15)·84
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-71}{2*-15}=\frac{-72}{-30}
=2+2/5
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+71}{2*-15}=\frac{70}{-30}
=-2+1/3
$