4x^2-23x+29=-2x+2

Solution for 4x^2-23x+29=-2x+2 equation:

4x^2-23x+29=-2x+2

We move all terms to the left:

4x^2-23x+29-(-2x+2)=0

We get rid of parentheses

4x^2-23x+2x-2+29=0

We add all the numbers together, and all the variables

4x^2-21x+27=0

a = 4; b = -21; c = +27;
Δ = b2-4ac
Δ = -212-4·4·27
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3}{2*4}=\frac{18}{8}
=2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3}{2*4}=\frac{24}{8}
=3
$