100=(-32x^2/4225)+x+190

Solution for 100=(-32x^2/4225)+x+190 equation:

100=(-32x^2/4225)+x+190

We move all terms to the left:

100-((-32x^2/4225)+x+190)=0


Domain of the equation: 4225)+x+190)!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-((-32x^2+100*4225)+x+190)=0


We calculate terms in parentheses: -((-32x^2+100*4225)+x+190), so:

(-32x^2+100*4225)+x+190

We get rid of parentheses

-32x^2+x+190+100*4225

We add all the numbers together, and all the variables

-32x^2+x+422690

Back to the equation:

-(-32x^2+x+422690)


We get rid of parentheses

32x^2-x-422690=0

We add all the numbers together, and all the variables

32x^2-1x-422690=0

a = 32; b = -1; c = -422690;
Δ = b2-4ac
Δ = -12-4·32·(-422690)
Δ = 54104321
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{54104321}}{2*32}=\frac{1-\sqrt{54104321}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{54104321}}{2*32}=\frac{1+\sqrt{54104321}}{64}
$