5x2+7x=x2+2

Solution for 5x2+7x=x2+2 equation:

5x^2+7x=x2+2

We move all terms to the left:

5x^2+7x-(x2+2)=0

We add all the numbers together, and all the variables

5x^2-(+x^2+2)+7x=0

We get rid of parentheses

5x^2-x^2+7x-2=0

We add all the numbers together, and all the variables

4x^2+7x-2=0

a = 4; b = 7; c = -2;
Δ = b2-4ac
Δ = 72-4·4·(-2)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-9}{2*4}=\frac{-16}{8}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+9}{2*4}=\frac{2}{8}
=1/4
$