(g-3)(g-5)=49

Solution for (g-3)(g-5)=49 equation:

(g-3)(g-5)=49

We move all terms to the left:

(g-3)(g-5)-(49)=0

We multiply parentheses ..

(+g^2-5g-3g+15)-49=0

We get rid of parentheses

g^2-5g-3g+15-49=0

We add all the numbers together, and all the variables

g^2-8g-34=0

a = 1; b = -8; c = -34;
Δ = b2-4ac
Δ = -82-4·1·(-34)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-10\sqrt{2}}{2*1}=\frac{8-10\sqrt{2}}{2}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+10\sqrt{2}}{2*1}=\frac{8+10\sqrt{2}}{2}
$