3(1-x)=-4x(x-5)-6

Solution for 3(1-x)=-4x(x-5)-6 equation:

3(1-x)=-4x(x-5)-6

We move all terms to the left:

3(1-x)-(-4x(x-5)-6)=0

We add all the numbers together, and all the variables

3(-1x+1)-(-4x(x-5)-6)=0

We multiply parentheses

-3x-(-4x(x-5)-6)+3=0


We calculate terms in parentheses: -(-4x(x-5)-6), so:

-4x(x-5)-6

We multiply parentheses

-4x^2+20x-6

Back to the equation:

-(-4x^2+20x-6)


We get rid of parentheses

4x^2-20x-3x+6+3=0

We add all the numbers together, and all the variables

4x^2-23x+9=0

a = 4; b = -23; c = +9;
Δ = b2-4ac
Δ = -232-4·4·9
Δ = 385
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{385}}{2*4}=\frac{23-\sqrt{385}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{385}}{2*4}=\frac{23+\sqrt{385}}{8}
$