7x+4x*x=8x-8x*x

Solution for 7x+4x*x=8x-8x*x equation:

7x+4x*x=8x-8x*x

We move all terms to the left:

7x+4x*x-(8x-8x*x)=0

We add all the numbers together, and all the variables

7x+4x*x-(+8x-8x*x)=0

Wy multiply elements

4x^2+7x-(+8x-8x*x)=0

We get rid of parentheses

4x^2+7x-8x+8x*x=0

We add all the numbers together, and all the variables

4x^2-1x+8x*x=0

Wy multiply elements

4x^2+8x^2-1x=0

We add all the numbers together, and all the variables

12x^2-1x=0

a = 12; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·12·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*12}=\frac{2}{24}
=1/12
$