5-5x2+11=3

Solution for 5-5x2+11=3 equation:

5-5x^2+11=3

We move all terms to the left:

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

We add all the numbers together, and all the variables

-5x^2+13=0

a = -5; b = 0; c = +13;
Δ = b2-4ac
Δ = 02-4·(-5)·13
Δ = 260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{65}}{2*-5}=\frac{0-2\sqrt{65}}{-10}
=-\frac{2\sqrt{65}}{-10}
=-\frac{\sqrt{65}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{65}}{2*-5}=\frac{0+2\sqrt{65}}{-10}
=\frac{2\sqrt{65}}{-10}
=\frac{\sqrt{65}}{-5}
$