5g^2-9g=2

Solution for 5g^2-9g=2 equation:

5g^2-9g=2

We move all terms to the left:

5g^2-9g-(2)=0

a = 5; b = -9; c = -2;
Δ = b2-4ac
Δ = -92-4·5·(-2)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-11}{2*5}=\frac{-2}{10}
=-1/5
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+11}{2*5}=\frac{20}{10}
=2
$