10=6x^2-32/54

Solution for 10=6x^2-32/54 equation:

10=6x^2-32/54

We move all terms to the left:

10-(6x^2-32/54)=0

We get rid of parentheses

-6x^2+10+32/54=0

We multiply all the terms by the denominator


-6x^2*54+32+10*54=0

We add all the numbers together, and all the variables

-6x^2*54+572=0

Wy multiply elements

-324x^2+572=0

a = -324; b = 0; c = +572;
Δ = b2-4ac
Δ = 02-4·(-324)·572
Δ = 741312
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:

$\sqrt{\Delta}=\sqrt{741312}=\sqrt{5184*143}=\sqrt{5184}*\sqrt{143}=72\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{143}}{2*-324}=\frac{0-72\sqrt{143}}{-648}
=-\frac{72\sqrt{143}}{-648}
=-\frac{\sqrt{143}}{-9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{143}}{2*-324}=\frac{0+72\sqrt{143}}{-648}
=\frac{72\sqrt{143}}{-648}
=\frac{\sqrt{143}}{-9}
$