0.10d+0.25d(d+7)=5.25

Solution for 0.10d+0.25d(d+7)=5.25 equation:

0.10d+0.25d(d+7)=5.25

We move all terms to the left:

0.10d+0.25d(d+7)-(5.25)=0

We add all the numbers together, and all the variables

0.10d+0.25d(d+7)-5.25=0

We multiply parentheses

0d^2+0.10d+0d-5.25=0

We add all the numbers together, and all the variables

d^2+1.1d-5.25=0

a = 1; b = 1.1; c = -5.25;
Δ = b2-4ac
Δ = 1.12-4·1·(-5.25)
Δ = 22.21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1.1)-\sqrt{22.21}}{2*1}=\frac{-1.1-\sqrt{22.21}}{2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.1)+\sqrt{22.21}}{2*1}=\frac{-1.1+\sqrt{22.21}}{2}
$