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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

2(g+9)g

We multiply parentheses

2g^2+18g

Back to the equation:

-(2g^2+18g)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-2g^2-8g+50=0

a = -2; b = -8; c = +50;
Δ = b2-4ac
Δ = -82-4·(-2)·50
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{29}}{2*-2}=\frac{8-4\sqrt{29}}{-4}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{29}}{2*-2}=\frac{8+4\sqrt{29}}{-4}
$