8x+3-10x=-2x(x-2)-4+3

Solution for 8x+3-10x=-2x(x-2)-4+3 equation:

8x+3-10x=-2x(x-2)-4+3

We move all terms to the left:

8x+3-10x-(-2x(x-2)-4+3)=0

We add all the numbers together, and all the variables

-2x-(-2x(x-2)-4+3)+3=0


We calculate terms in parentheses: -(-2x(x-2)-4+3), so:

-2x(x-2)-4+3

We add all the numbers together, and all the variables

-2x(x-2)-1

We multiply parentheses

-2x^2+4x-1

Back to the equation:

-(-2x^2+4x-1)


We get rid of parentheses

2x^2-4x-2x+1+3=0

We add all the numbers together, and all the variables

2x^2-6x+4=0

a = 2; b = -6; c = +4;
Δ = b2-4ac
Δ = -62-4·2·4
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2}{2*2}=\frac{8}{4}
=2
$