G(x)=(-5x-1)(2x+8)

Solution for G(x)=(-5x-1)(2x+8) equation:

(G)=(-5G-1)(2G+8)

We move all terms to the left:

(G)-((-5G-1)(2G+8))=0

We multiply parentheses ..

-((-10G^2-40G-2G-8))+G=0


We calculate terms in parentheses: -((-10G^2-40G-2G-8)), so:

(-10G^2-40G-2G-8)

We get rid of parentheses

-10G^2-40G-2G-8

We add all the numbers together, and all the variables

-10G^2-42G-8

Back to the equation:

-(-10G^2-42G-8)


We get rid of parentheses

10G^2+42G+G+8=0

We add all the numbers together, and all the variables

10G^2+43G+8=0

a = 10; b = 43; c = +8;
Δ = b2-4ac
Δ = 432-4·10·8
Δ = 1529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-\sqrt{1529}}{2*10}=\frac{-43-\sqrt{1529}}{20}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+\sqrt{1529}}{2*10}=\frac{-43+\sqrt{1529}}{20}
$