20g(-8g-15)=3(4g-5)

Solution for 20g(-8g-15)=3(4g-5) equation:

20g(-8g-15)=3(4g-5)

We move all terms to the left:

20g(-8g-15)-(3(4g-5))=0

We multiply parentheses

-160g^2-300g-(3(4g-5))=0


We calculate terms in parentheses: -(3(4g-5)), so:

3(4g-5)

We multiply parentheses

12g-15

Back to the equation:

-(12g-15)


We get rid of parentheses

-160g^2-300g-12g+15=0

We add all the numbers together, and all the variables

-160g^2-312g+15=0

a = -160; b = -312; c = +15;
Δ = b2-4ac
Δ = -3122-4·(-160)·15
Δ = 106944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{106944}=\sqrt{64*1671}=\sqrt{64}*\sqrt{1671}=8\sqrt{1671}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-312)-8\sqrt{1671}}{2*-160}=\frac{312-8\sqrt{1671}}{-320}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-312)+8\sqrt{1671}}{2*-160}=\frac{312+8\sqrt{1671}}{-320}
$