(3x^2-10)/5=12x

Solution for (3x^2-10)/5=12x equation:

(3x^2-10)/5=12x

We move all terms to the left:

(3x^2-10)/5-(12x)=0

We add all the numbers together, and all the variables

-12x+(3x^2-10)/5=0

We multiply all the terms by the denominator


-12x*5+(3x^2-10)=0

Wy multiply elements

-60x+(3x^2-10)=0

We get rid of parentheses

3x^2-60x-10=0

a = 3; b = -60; c = -10;
Δ = b2-4ac
Δ = -602-4·3·(-10)
Δ = 3720
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:

$\sqrt{\Delta}=\sqrt{3720}=\sqrt{4*930}=\sqrt{4}*\sqrt{930}=2\sqrt{930}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{930}}{2*3}=\frac{60-2\sqrt{930}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{930}}{2*3}=\frac{60+2\sqrt{930}}{6}
$