x2-7x+38=5x+3

Solution for x2-7x+38=5x+3 equation:

x2-7x+38=5x+3

We move all terms to the left:

x2-7x+38-(5x+3)=0

We add all the numbers together, and all the variables

x^2-7x-(5x+3)+38=0

We get rid of parentheses

x^2-7x-5x-3+38=0

We add all the numbers together, and all the variables

x^2-12x+35=0

a = 1; b = -12; c = +35;
Δ = b2-4ac
Δ = -122-4·1·35
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2}{2*1}=\frac{10}{2}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2}{2*1}=\frac{14}{2}
=7
$