11-5x^2+3x=3

Solution for 11-5x^2+3x=3 equation:

11-5x^2+3x=3

We move all terms to the left:

11-5x^2+3x-(3)=0

We add all the numbers together, and all the variables

-5x^2+3x+8=0

a = -5; b = 3; c = +8;
Δ = b2-4ac
Δ = 32-4·(-5)·8
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-13}{2*-5}=\frac{-16}{-10}
=1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+13}{2*-5}=\frac{10}{-10}
=-1
$