2x2-10=x/3+40

Solution for 2x2-10=x/3+40 equation:

2x^2-10=x/3+40

We move all terms to the left:

2x^2-10-(x/3+40)=0

We get rid of parentheses

2x^2-x/3-40-10=0

We multiply all the terms by the denominator


2x^2*3-x-40*3-10*3=0

We add all the numbers together, and all the variables

2x^2*3-1x-150=0

Wy multiply elements

6x^2-1x-150=0

a = 6; b = -1; c = -150;
Δ = b2-4ac
Δ = -12-4·6·(-150)
Δ = 3601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{3601}}{2*6}=\frac{1-\sqrt{3601}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{3601}}{2*6}=\frac{1+\sqrt{3601}}{12}
$