2x^2=1.2416*10^-9(5+5x-10x^2)

Solution for 2x^2=1.2416*10^-9(5+5x-10x^2) equation:

2x^2=1.2416*10^-9(5+5x-10x^2)

We move all terms to the left:

2x^2-(1.2416*10^-9(5+5x-10x^2))=0


We calculate terms in parentheses: -(1.2416*10^-9(5+5x-10x^2)), so:

1.2416*10^-9(5+5x-10x^2)

determiningTheFunctionDomain
-9(5+5x-10x^2)+1.2416*10^

We add all the numbers together, and all the variables

-9(5+5x-10x^2)

We multiply parentheses

90x^2-45x-45

Back to the equation:

-(90x^2-45x-45)


We get rid of parentheses

2x^2-90x^2+45x+45=0

We add all the numbers together, and all the variables

-88x^2+45x+45=0

a = -88; b = 45; c = +45;
Δ = b2-4ac
Δ = 452-4·(-88)·45
Δ = 17865
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:

$\sqrt{\Delta}=\sqrt{17865}=\sqrt{9*1985}=\sqrt{9}*\sqrt{1985}=3\sqrt{1985}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{1985}}{2*-88}=\frac{-45-3\sqrt{1985}}{-176}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{1985}}{2*-88}=\frac{-45+3\sqrt{1985}}{-176}
$