(5d+7)(d+5)=23

Solution for (5d+7)(d+5)=23 equation:

(5d+7)(d+5)=23

We move all terms to the left:

(5d+7)(d+5)-(23)=0

We multiply parentheses ..

(+5d^2+25d+7d+35)-23=0

We get rid of parentheses

5d^2+25d+7d+35-23=0

We add all the numbers together, and all the variables

5d^2+32d+12=0

a = 5; b = 32; c = +12;
Δ = b2-4ac
Δ = 322-4·5·12
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-28}{2*5}=\frac{-60}{10}
=-6
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+28}{2*5}=\frac{-4}{10}
=-2/5
$