(1-x)(4x+17)=3x

Solution for (1-x)(4x+17)=3x equation:

(1-x)(4x+17)=3x

We move all terms to the left:

(1-x)(4x+17)-(3x)=0

We add all the numbers together, and all the variables

(-1x+1)(4x+17)-3x=0

We add all the numbers together, and all the variables

-3x+(-1x+1)(4x+17)=0

We multiply parentheses ..

(-4x^2-17x+4x+17)-3x=0

We get rid of parentheses

-4x^2-17x+4x-3x+17=0

We add all the numbers together, and all the variables

-4x^2-16x+17=0

a = -4; b = -16; c = +17;
Δ = b2-4ac
Δ = -162-4·(-4)·17
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{33}}{2*-4}=\frac{16-4\sqrt{33}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{33}}{2*-4}=\frac{16+4\sqrt{33}}{-8}
$