5x^2+3x+1=x^2+12+10

Solution for 5x^2+3x+1=x^2+12+10 equation:

5x^2+3x+1=x^2+12+10

We move all terms to the left:

5x^2+3x+1-(x^2+12+10)=0

We get rid of parentheses

5x^2-x^2+3x-12-10+1=0

We add all the numbers together, and all the variables

4x^2+3x-21=0

a = 4; b = 3; c = -21;
Δ = b2-4ac
Δ = 32-4·4·(-21)
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{345}}{2*4}=\frac{-3-\sqrt{345}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{345}}{2*4}=\frac{-3+\sqrt{345}}{8}
$