6(-2g-1)=-(13g+2)g=

Solution for 6(-2g-1)=-(13g+2)g= equation:

6(-2g-1)=-(13g+2)g=

We move all terms to the left:

6(-2g-1)-(-(13g+2)g)=0

We multiply parentheses

-12g-(-(13g+2)g)-6=0


We calculate terms in parentheses: -(-(13g+2)g), so:

-(13g+2)g

We multiply parentheses

-13g^2-2g

Back to the equation:

-(-13g^2-2g)


We get rid of parentheses

13g^2+2g-12g-6=0

We add all the numbers together, and all the variables

13g^2-10g-6=0

a = 13; b = -10; c = -6;
Δ = b2-4ac
Δ = -102-4·13·(-6)
Δ = 412
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:

$\sqrt{\Delta}=\sqrt{412}=\sqrt{4*103}=\sqrt{4}*\sqrt{103}=2\sqrt{103}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{103}}{2*13}=\frac{10-2\sqrt{103}}{26}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{103}}{2*13}=\frac{10+2\sqrt{103}}{26}
$