4x+8=x^2-3x+7

Solution for 4x+8=x^2-3x+7 equation:

4x+8=x^2-3x+7

We move all terms to the left:

4x+8-(x^2-3x+7)=0

We get rid of parentheses

-x^2+4x+3x-7+8=0

We add all the numbers together, and all the variables

-1x^2+7x+1=0

a = -1; b = 7; c = +1;
Δ = b2-4ac
Δ = 72-4·(-1)·1
Δ = 53
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{-(7)-\sqrt{53}}{2*-1}=\frac{-7-\sqrt{53}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{53}}{2*-1}=\frac{-7+\sqrt{53}}{-2}
$