4x(x-2)=-3x+27

Solution for 4x(x-2)=-3x+27 equation:

4x(x-2)=-3x+27

We move all terms to the left:

4x(x-2)-(-3x+27)=0

We multiply parentheses

4x^2-8x-(-3x+27)=0

We get rid of parentheses

4x^2-8x+3x-27=0

We add all the numbers together, and all the variables

4x^2-5x-27=0

a = 4; b = -5; c = -27;
Δ = b2-4ac
Δ = -52-4·4·(-27)
Δ = 457
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{-(-5)-\sqrt{457}}{2*4}=\frac{5-\sqrt{457}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{457}}{2*4}=\frac{5+\sqrt{457}}{8}
$