6x^2/5-8=46

Solution for 6x^2/5-8=46 equation:

6x^2/5-8=46

We move all terms to the left:

6x^2/5-8-(46)=0

We add all the numbers together, and all the variables

6x^2/5-54=0

We multiply all the terms by the denominator


6x^2-54*5=0

We add all the numbers together, and all the variables

6x^2-270=0

a = 6; b = 0; c = -270;
Δ = b2-4ac
Δ = 02-4·6·(-270)
Δ = 6480
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:

$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{5}}{2*6}=\frac{0-36\sqrt{5}}{12}
=-\frac{36\sqrt{5}}{12}
=-3\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{5}}{2*6}=\frac{0+36\sqrt{5}}{12}
=\frac{36\sqrt{5}}{12}
=3\sqrt{5}
$