(5d+8)(10d-31)=(10d+11)

Solution for (5d+8)(10d-31)=(10d+11) equation:

(5d+8)(10d-31)=(10d+11)

We move all terms to the left:

(5d+8)(10d-31)-((10d+11))=0

We multiply parentheses ..

(+50d^2-155d+80d-248)-((10d+11))=0


We calculate terms in parentheses: -((10d+11)), so:

(10d+11)

We get rid of parentheses

10d+11

Back to the equation:

-(10d+11)


We get rid of parentheses

50d^2-155d+80d-10d-248-11=0

We add all the numbers together, and all the variables

50d^2-85d-259=0

a = 50; b = -85; c = -259;
Δ = b2-4ac
Δ = -852-4·50·(-259)
Δ = 59025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{59025}=\sqrt{25*2361}=\sqrt{25}*\sqrt{2361}=5\sqrt{2361}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-5\sqrt{2361}}{2*50}=\frac{85-5\sqrt{2361}}{100}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+5\sqrt{2361}}{2*50}=\frac{85+5\sqrt{2361}}{100}
$