d^2/25+4d-250=150

Solution for d^2/25+4d-250=150 equation:

d^2/25+4d-250=150

We move all terms to the left:

d^2/25+4d-250-(150)=0

We add all the numbers together, and all the variables

d^2/25+4d-400=0

We multiply all the terms by the denominator


d^2+4d*25-400*25=0

We add all the numbers together, and all the variables

d^2+4d*25-10000=0

Wy multiply elements

d^2+100d-10000=0

a = 1; b = 100; c = -10000;
Δ = b2-4ac
Δ = 1002-4·1·(-10000)
Δ = 50000
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:

$\sqrt{\Delta}=\sqrt{50000}=\sqrt{10000*5}=\sqrt{10000}*\sqrt{5}=100\sqrt{5}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100\sqrt{5}}{2*1}=\frac{-100-100\sqrt{5}}{2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100\sqrt{5}}{2*1}=\frac{-100+100\sqrt{5}}{2}
$