25=(2d+24)(5-d)

Solution for 25=(2d+24)(5-d) equation:

25=(2d+24)(5-d)

We move all terms to the left:

25-((2d+24)(5-d))=0

We add all the numbers together, and all the variables

-((2d+24)(-1d+5))+25=0

We multiply parentheses ..

-((-2d^2+10d-24d+120))+25=0


We calculate terms in parentheses: -((-2d^2+10d-24d+120)), so:

(-2d^2+10d-24d+120)

We get rid of parentheses

-2d^2+10d-24d+120

We add all the numbers together, and all the variables

-2d^2-14d+120

Back to the equation:

-(-2d^2-14d+120)


We get rid of parentheses

2d^2+14d-120+25=0

We add all the numbers together, and all the variables

2d^2+14d-95=0

a = 2; b = 14; c = -95;
Δ = b2-4ac
Δ = 142-4·2·(-95)
Δ = 956
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:

$\sqrt{\Delta}=\sqrt{956}=\sqrt{4*239}=\sqrt{4}*\sqrt{239}=2\sqrt{239}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{239}}{2*2}=\frac{-14-2\sqrt{239}}{4}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{239}}{2*2}=\frac{-14+2\sqrt{239}}{4}
$