2x^2+4=-5x+1

Solution for 2x^2+4=-5x+1 equation:

2x^2+4=-5x+1

We move all terms to the left:

2x^2+4-(-5x+1)=0

We get rid of parentheses

2x^2+5x-1+4=0

We add all the numbers together, and all the variables

2x^2+5x+3=0

a = 2; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·2·3
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-1}{2*2}=\frac{-6}{4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*2}=\frac{-4}{4}
=-1
$