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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-9x-9=0

a = 4; b = -9; c = -9;
Δ = b2-4ac
Δ = -92-4·4·(-9)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*4}=\frac{-6}{8}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*4}=\frac{24}{8}
=3
$