5g(8g+6)=40g+6

Solution for 5g(8g+6)=40g+6 equation:

5g(8g+6)=40g+6

We move all terms to the left:

5g(8g+6)-(40g+6)=0

We multiply parentheses

40g^2+30g-(40g+6)=0

We get rid of parentheses

40g^2+30g-40g-6=0

We add all the numbers together, and all the variables

40g^2-10g-6=0

a = 40; b = -10; c = -6;
Δ = b2-4ac
Δ = -102-4·40·(-6)
Δ = 1060
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:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{265}}{2*40}=\frac{10-2\sqrt{265}}{80}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{265}}{2*40}=\frac{10+2\sqrt{265}}{80}
$