4-3x(5-x)=2-7x

Solution for 4-3x(5-x)=2-7x equation:

4-3x(5-x)=2-7x

We move all terms to the left:

4-3x(5-x)-(2-7x)=0

We add all the numbers together, and all the variables

-3x(-1x+5)-(-7x+2)+4=0

We multiply parentheses

3x^2-15x-(-7x+2)+4=0

We get rid of parentheses

3x^2-15x+7x-2+4=0

We add all the numbers together, and all the variables

3x^2-8x+2=0

a = 3; b = -8; c = +2;
Δ = b2-4ac
Δ = -82-4·3·2
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{10}}{2*3}=\frac{8-2\sqrt{10}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{10}}{2*3}=\frac{8+2\sqrt{10}}{6}
$