5x+4x^2=8x+x^2

Solution for 5x+4x^2=8x+x^2 equation:

5x+4x^2=8x+x^2

We move all terms to the left:

5x+4x^2-(8x+x^2)=0

We get rid of parentheses

4x^2-x^2-8x+5x=0

We add all the numbers together, and all the variables

3x^2-3x=0

a = 3; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·3·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*3}=\frac{6}{6}
=1
$