3g+6(g-2)=-10g(g-4)-2g

Solution for 3g+6(g-2)=-10g(g-4)-2g equation:

3g+6(g-2)=-10g(g-4)-2g

We move all terms to the left:

3g+6(g-2)-(-10g(g-4)-2g)=0

We multiply parentheses

3g+6g-(-10g(g-4)-2g)-12=0


We calculate terms in parentheses: -(-10g(g-4)-2g), so:

-10g(g-4)-2g

We add all the numbers together, and all the variables

-2g-10g(g-4)

We multiply parentheses

-10g^2-2g+40g

We add all the numbers together, and all the variables

-10g^2+38g

Back to the equation:

-(-10g^2+38g)


We add all the numbers together, and all the variables

-(-10g^2+38g)+9g-12=0

We get rid of parentheses

10g^2-38g+9g-12=0

We add all the numbers together, and all the variables

10g^2-29g-12=0

a = 10; b = -29; c = -12;
Δ = b2-4ac
Δ = -292-4·10·(-12)
Δ = 1321
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{-(-29)-\sqrt{1321}}{2*10}=\frac{29-\sqrt{1321}}{20}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{1321}}{2*10}=\frac{29+\sqrt{1321}}{20}
$