3-2x(x+5)=-20

Solution for 3-2x(x+5)=-20 equation:

3-2x(x+5)=-20

We move all terms to the left:

3-2x(x+5)-(-20)=0

We add all the numbers together, and all the variables

-2x(x+5)+23=0

We multiply parentheses

-2x^2-10x+23=0

a = -2; b = -10; c = +23;
Δ = b2-4ac
Δ = -102-4·(-2)·23
Δ = 284
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{71}}{2*-2}=\frac{10-2\sqrt{71}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{71}}{2*-2}=\frac{10+2\sqrt{71}}{-4}
$