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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = -1; c = +5;
Δ = b2-4ac
Δ = -12-4·(-1)·5
Δ = 21
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{-(-1)-\sqrt{21}}{2*-1}=\frac{1-\sqrt{21}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{21}}{2*-1}=\frac{1+\sqrt{21}}{-2}
$