(2.5)^2=d^2+(1.5)^2

Solution for (2.5)^2=d^2+(1.5)^2 equation:

(2.5)^2=d^2+(1.5)^2

We move all terms to the left:

(2.5)^2-(d^2+(1.5)^2)=0

We add all the numbers together, and all the variables

-(d^2+(1.5)^2)+6.25=0


We calculate terms in parentheses: -(d^2+(1.5)^2), so:

d^2+(1.5)^2

We add all the numbers together, and all the variables

d^2+2.25

Back to the equation:

-(d^2+2.25)


We get rid of parentheses

-d^2-2.25+6.25=0

We add all the numbers together, and all the variables

-1d^2+4=0

a = -1; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-1)·4
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*-1}=\frac{-4}{-2}
=+2
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*-1}=\frac{4}{-2}
=-2
$