11x^2-13x=8x-3x^2

Solution for 11x^2-13x=8x-3x^2 equation:

11x^2-13x=8x-3x^2

We move all terms to the left:

11x^2-13x-(8x-3x^2)=0

We get rid of parentheses

11x^2+3x^2-8x-13x=0

We add all the numbers together, and all the variables

14x^2-21x=0

a = 14; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·14·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*14}=\frac{0}{28}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*14}=\frac{42}{28}
=1+1/2
$