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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

3x^2-10x-10=0

a = 3; b = -10; c = -10;
Δ = b2-4ac
Δ = -102-4·3·(-10)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{55}}{2*3}=\frac{10-2\sqrt{55}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{55}}{2*3}=\frac{10+2\sqrt{55}}{6}
$