8x-10x(3-x)=42

Solution for 8x-10x(3-x)=42 equation:

8x-10x(3-x)=42

We move all terms to the left:

8x-10x(3-x)-(42)=0

We add all the numbers together, and all the variables

8x-10x(-1x+3)-42=0

We multiply parentheses

10x^2+8x-30x-42=0

We add all the numbers together, and all the variables

10x^2-22x-42=0

a = 10; b = -22; c = -42;
Δ = b2-4ac
Δ = -222-4·10·(-42)
Δ = 2164
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:

$\sqrt{\Delta}=\sqrt{2164}=\sqrt{4*541}=\sqrt{4}*\sqrt{541}=2\sqrt{541}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{541}}{2*10}=\frac{22-2\sqrt{541}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{541}}{2*10}=\frac{22+2\sqrt{541}}{20}
$