4x2-23x+27=-3x+6

Solution for 4x2-23x+27=-3x+6 equation:

4x^2-23x+27=-3x+6

We move all terms to the left:

4x^2-23x+27-(-3x+6)=0

We get rid of parentheses

4x^2-23x+3x-6+27=0

We add all the numbers together, and all the variables

4x^2-20x+21=0

a = 4; b = -20; c = +21;
Δ = b2-4ac
Δ = -202-4·4·21
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8}{2*4}=\frac{12}{8}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8}{2*4}=\frac{28}{8}
=3+1/2
$