10g(g+5)=2(g+9)

Solution for 10g(g+5)=2(g+9) equation:

10g(g+5)=2(g+9)

We move all terms to the left:

10g(g+5)-(2(g+9))=0

We multiply parentheses

10g^2+50g-(2(g+9))=0


We calculate terms in parentheses: -(2(g+9)), so:

2(g+9)

We multiply parentheses

2g+18

Back to the equation:

-(2g+18)


We get rid of parentheses

10g^2+50g-2g-18=0

We add all the numbers together, and all the variables

10g^2+48g-18=0

a = 10; b = 48; c = -18;
Δ = b2-4ac
Δ = 482-4·10·(-18)
Δ = 3024
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:

$\sqrt{\Delta}=\sqrt{3024}=\sqrt{144*21}=\sqrt{144}*\sqrt{21}=12\sqrt{21}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-12\sqrt{21}}{2*10}=\frac{-48-12\sqrt{21}}{20}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+12\sqrt{21}}{2*10}=\frac{-48+12\sqrt{21}}{20}
$