2x^2-7x+3=x^2+2x+13

Solution for 2x^2-7x+3=x^2+2x+13 equation:

2x^2-7x+3=x^2+2x+13

We move all terms to the left:

2x^2-7x+3-(x^2+2x+13)=0

We get rid of parentheses

2x^2-x^2-7x-2x-13+3=0

We add all the numbers together, and all the variables

x^2-9x-10=0

a = 1; b = -9; c = -10;
Δ = b2-4ac
Δ = -92-4·1·(-10)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-11}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+11}{2*1}=\frac{20}{2}
=10
$