13x2-5x=13-3x+3

Solution for 13x2-5x=13-3x+3 equation:

13x^2-5x=13-3x+3

We move all terms to the left:

13x^2-5x-(13-3x+3)=0

We add all the numbers together, and all the variables

13x^2-5x-(-3x+16)=0

We get rid of parentheses

13x^2-5x+3x-16=0

We add all the numbers together, and all the variables

13x^2-2x-16=0

a = 13; b = -2; c = -16;
Δ = b2-4ac
Δ = -22-4·13·(-16)
Δ = 836
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:

$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{209}}{2*13}=\frac{2-2\sqrt{209}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{209}}{2*13}=\frac{2+2\sqrt{209}}{26}
$