8g+6(g-2)=-10(g-4)2g

Solution for 8g+6(g-2)=-10(g-4)2g equation:

8g+6(g-2)=-10(g-4)2g

We move all terms to the left:

8g+6(g-2)-(-10(g-4)2g)=0

We multiply parentheses

8g+6g-(-10(g-4)2g)-12=0


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

-10(g-4)2g

We multiply parentheses

-20g^2+80g

Back to the equation:

-(-20g^2+80g)


We add all the numbers together, and all the variables

-(-20g^2+80g)+14g-12=0

We get rid of parentheses

20g^2-80g+14g-12=0

We add all the numbers together, and all the variables

20g^2-66g-12=0

a = 20; b = -66; c = -12;
Δ = b2-4ac
Δ = -662-4·20·(-12)
Δ = 5316
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:

$\sqrt{\Delta}=\sqrt{5316}=\sqrt{4*1329}=\sqrt{4}*\sqrt{1329}=2\sqrt{1329}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1329}}{2*20}=\frac{66-2\sqrt{1329}}{40}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1329}}{2*20}=\frac{66+2\sqrt{1329}}{40}
$