Answer:The solutions are: 5 and 7
Explanation:First we would need to put the equation in the standard form which is:
ax² + bx + c = 0
This can be done as follows:
x² - 7x + 38 = 5x + 3
x² - 7x + 38 - 5x - 3 = 0
x² - 12x + 35 = 0
By comparison:
a = 1
b = -12
c = 35
Now, to get the roots, we would need to use the quadratic formula attached in the images.
By substitution, we would find that:\
either x =
![\frac{12+ \sqrt{(-12)^2-4(1)(35)} }{2(1)} = 7](https://tex.z-dn.net/?f=%20%5Cfrac%7B12%2B%20%5Csqrt%7B%28-12%29%5E2-4%281%29%2835%29%7D%20%7D%7B2%281%29%7D%20%3D%207)
or x =
![\frac{12- \sqrt{(-12)^2-4(1)(35)} }{2(1)} = 5](https://tex.z-dn.net/?f=%20%5Cfrac%7B12-%20%5Csqrt%7B%28-12%29%5E2-4%281%29%2835%29%7D%20%7D%7B2%281%29%7D%20%3D%205)
Hope this helps :)