6w^2-9=153

Solution for 6w^2-9=153 equation:

6w^2-9=153

We move all terms to the left:

6w^2-9-(153)=0

We add all the numbers together, and all the variables

6w^2-162=0

a = 6; b = 0; c = -162;
Δ = b2-4ac
Δ = 02-4·6·(-162)
Δ = 3888
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3888}=\sqrt{1296*3}=\sqrt{1296}*\sqrt{3}=36\sqrt{3}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{3}}{2*6}=\frac{0-36\sqrt{3}}{12}
=-\frac{36\sqrt{3}}{12}
=-3\sqrt{3}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{3}}{2*6}=\frac{0+36\sqrt{3}}{12}
=\frac{36\sqrt{3}}{12}
=3\sqrt{3}
$