3575-x^2-10x=0

Solution for 3575-x^2-10x=0 equation:

3575-x^2-10x=0

We add all the numbers together, and all the variables

-1x^2-10x+3575=0

a = -1; b = -10; c = +3575;
Δ = b2-4ac
Δ = -102-4·(-1)·3575
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-120}{2*-1}=\frac{-110}{-2}
=+55
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+120}{2*-1}=\frac{130}{-2}
=-65
$