6x^2-7=153

Solution for 6x^2-7=153 equation:

6x^2-7=153

We move all terms to the left:

6x^2-7-(153)=0

We add all the numbers together, and all the variables

6x^2-160=0

a = 6; b = 0; c = -160;
Δ = b2-4ac
Δ = 02-4·6·(-160)
Δ = 3840
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{15}}{2*6}=\frac{0-16\sqrt{15}}{12}
=-\frac{16\sqrt{15}}{12}
=-\frac{4\sqrt{15}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{15}}{2*6}=\frac{0+16\sqrt{15}}{12}
=\frac{16\sqrt{15}}{12}
=\frac{4\sqrt{15}}{3}
$