10-5(x-11)x=3

Solution for 10-5(x-11)x=3 equation:

10-5(x-11)x=3

We move all terms to the left:

10-5(x-11)x-(3)=0

We add all the numbers together, and all the variables

-5(x-11)x+7=0

We multiply parentheses

-5x^2+55x+7=0

a = -5; b = 55; c = +7;
Δ = b2-4ac
Δ = 552-4·(-5)·7
Δ = 3165
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{-(55)-\sqrt{3165}}{2*-5}=\frac{-55-\sqrt{3165}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{3165}}{2*-5}=\frac{-55+\sqrt{3165}}{-10}
$