((-32x^2)/3025)+x+220=100

Solution for ((-32x^2)/3025)+x+220=100 equation:

((-32x^2)/3025)+x+220=100

We move all terms to the left:

((-32x^2)/3025)+x+220-(100)=0

We add all the numbers together, and all the variables

((-32x^2)/3025)+x+120=0

We multiply all the terms by the denominator


((-32x^2)+x*3025)+120*3025)=0


We calculate terms in parentheses: +((-32x^2)+x*3025), so:

(-32x^2)+x*3025

Wy multiply elements

(-32x^2)+3025x

We get rid of parentheses

-32x^2+3025x

Back to the equation:

+(-32x^2+3025x)


We add all the numbers together, and all the variables

(-32x^2+3025x)=0

We get rid of parentheses

-32x^2+3025x=0

a = -32; b = 3025; c = 0;
Δ = b2-4ac
Δ = 30252-4·(-32)·0
Δ = 9150625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9150625}=3025$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3025)-3025}{2*-32}=\frac{-6050}{-64}
=94+17/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3025)+3025}{2*-32}=\frac{0}{-64}
=0
$