4(2-x)=5(x2)

Solution for 4(2-x)=5(x2) equation:

4(2-x)=5(x2)

We move all terms to the left:

4(2-x)-(5(x2))=0

determiningTheFunctionDomain
4(2-x)-5x2=0

We add all the numbers together, and all the variables

4(-1x+2)-5x2=0

We add all the numbers together, and all the variables

-5x^2+4(-1x+2)=0

We multiply parentheses

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

a = -5; b = -4; c = +8;
Δ = b2-4ac
Δ = -42-4·(-5)·8
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{11}}{2*-5}=\frac{4-4\sqrt{11}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{11}}{2*-5}=\frac{4+4\sqrt{11}}{-10}
$