7d2-45+13=2d-2

Solution for 7d2-45+13=2d-2 equation:

7d^2-45+13=2d-2

We move all terms to the left:

7d^2-45+13-(2d-2)=0

We add all the numbers together, and all the variables

7d^2-(2d-2)-32=0

We get rid of parentheses

7d^2-2d+2-32=0

We add all the numbers together, and all the variables

7d^2-2d-30=0

a = 7; b = -2; c = -30;
Δ = b2-4ac
Δ = -22-4·7·(-30)
Δ = 844
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:

$\sqrt{\Delta}=\sqrt{844}=\sqrt{4*211}=\sqrt{4}*\sqrt{211}=2\sqrt{211}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{211}}{2*7}=\frac{2-2\sqrt{211}}{14}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{211}}{2*7}=\frac{2+2\sqrt{211}}{14}
$