(3d+5)(d+7)=90

Solution for (3d+5)(d+7)=90 equation:

(3d+5)(d+7)=90

We move all terms to the left:

(3d+5)(d+7)-(90)=0

We multiply parentheses ..

(+3d^2+21d+5d+35)-90=0

We get rid of parentheses

3d^2+21d+5d+35-90=0

We add all the numbers together, and all the variables

3d^2+26d-55=0

a = 3; b = 26; c = -55;
Δ = b2-4ac
Δ = 262-4·3·(-55)
Δ = 1336
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:

$\sqrt{\Delta}=\sqrt{1336}=\sqrt{4*334}=\sqrt{4}*\sqrt{334}=2\sqrt{334}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{334}}{2*3}=\frac{-26-2\sqrt{334}}{6}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{334}}{2*3}=\frac{-26+2\sqrt{334}}{6}
$