(x+3.7)(8.6-x)=0

Solution for (x+3.7)(8.6-x)=0 equation:

(x+3.7)(8.6-x)=0

We add all the numbers together, and all the variables

(x+3.7)(-1x+8.6)=0

We multiply parentheses ..

(-1x^2+8.6x-3.7x+31.82)=0

We get rid of parentheses

-1x^2+8.6x-3.7x+31.82=0

We add all the numbers together, and all the variables

-1x^2+4.9x+31.82=0

a = -1; b = 4.9; c = +31.82;
Δ = b2-4ac
Δ = 4.92-4·(-1)·31.82
Δ = 151.29
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4.9)-\sqrt{151.29}}{2*-1}=\frac{-4.9-\sqrt{151.29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.9)+\sqrt{151.29}}{2*-1}=\frac{-4.9+\sqrt{151.29}}{-2}
$