2x^2-5x-29=-x+1

Solution for 2x^2-5x-29=-x+1 equation:

2x^2-5x-29=-x+1

We move all terms to the left:

2x^2-5x-29-(-x+1)=0

We add all the numbers together, and all the variables

2x^2-5x-(-1x+1)-29=0

We get rid of parentheses

2x^2-5x+1x-1-29=0

We add all the numbers together, and all the variables

2x^2-4x-30=0

a = 2; b = -4; c = -30;
Δ = b2-4ac
Δ = -42-4·2·(-30)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16}{2*2}=\frac{20}{4}
=5
$