25+10d(117-d)=1575

Solution for 25+10d(117-d)=1575 equation:

25+10d(117-d)=1575

We move all terms to the left:

25+10d(117-d)-(1575)=0

We add all the numbers together, and all the variables

10d(-1d+117)+25-1575=0

We add all the numbers together, and all the variables

10d(-1d+117)-1550=0

We multiply parentheses

-10d^2+1170d-1550=0

a = -10; b = 1170; c = -1550;
Δ = b2-4ac
Δ = 11702-4·(-10)·(-1550)
Δ = 1306900
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:

$\sqrt{\Delta}=\sqrt{1306900}=\sqrt{100*13069}=\sqrt{100}*\sqrt{13069}=10\sqrt{13069}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1170)-10\sqrt{13069}}{2*-10}=\frac{-1170-10\sqrt{13069}}{-20}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1170)+10\sqrt{13069}}{2*-10}=\frac{-1170+10\sqrt{13069}}{-20}
$