2d(d-5)-3(5-d)=0

Solution for 2d(d-5)-3(5-d)=0 equation:

2d(d-5)-3(5-d)=0

We add all the numbers together, and all the variables

2d(d-5)-3(-1d+5)=0

We multiply parentheses

2d^2-10d+3d-15=0

We add all the numbers together, and all the variables

2d^2-7d-15=0

a = 2; b = -7; c = -15;
Δ = b2-4ac
Δ = -72-4·2·(-15)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*2}=\frac{-6}{4}
=-1+1/2
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*2}=\frac{20}{4}
=5
$