0=-76/2x^2+150

Solution for 0=-76/2x^2+150 equation:

0=-76/2x^2+150

We move all terms to the left:

0-(-76/2x^2+150)=0


Domain of the equation: 2x^2+150)!=0

x∈R


We add all the numbers together, and all the variables

-(-76/2x^2+150)=0

We get rid of parentheses

76/2x^2-150=0

We multiply all the terms by the denominator


-150*2x^2+76=0

Wy multiply elements

-300x^2+76=0

a = -300; b = 0; c = +76;
Δ = b2-4ac
Δ = 02-4·(-300)·76
Δ = 91200
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:

$\sqrt{\Delta}=\sqrt{91200}=\sqrt{1600*57}=\sqrt{1600}*\sqrt{57}=40\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{57}}{2*-300}=\frac{0-40\sqrt{57}}{-600}
=-\frac{40\sqrt{57}}{-600}
=-\frac{\sqrt{57}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{57}}{2*-300}=\frac{0+40\sqrt{57}}{-600}
=\frac{40\sqrt{57}}{-600}
=\frac{\sqrt{57}}{-15}
$