150d-d^2=5625/2

Solution for 150d-d^2=5625/2 equation:

150d-d^2=5625/2

We move all terms to the left:

150d-d^2-(5625/2)=0

We add all the numbers together, and all the variables

-d^2+150d-(+5625/2)=0

We add all the numbers together, and all the variables

-1d^2+150d-(+5625/2)=0

We get rid of parentheses

-1d^2+150d-5625/2=0

We multiply all the terms by the denominator


-1d^2*2+150d*2-5625=0

Wy multiply elements

-2d^2+300d-5625=0

a = -2; b = 300; c = -5625;
Δ = b2-4ac
Δ = 3002-4·(-2)·(-5625)
Δ = 45000
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:

$\sqrt{\Delta}=\sqrt{45000}=\sqrt{22500*2}=\sqrt{22500}*\sqrt{2}=150\sqrt{2}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-150\sqrt{2}}{2*-2}=\frac{-300-150\sqrt{2}}{-4}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+150\sqrt{2}}{2*-2}=\frac{-300+150\sqrt{2}}{-4}
$