Question

What is 3/4(x2+4x+6)=13x-2

Answer 1

Answer:

$x_1=12.65\\\\x_2=0.685$

Step-by-step explanation:

$\frac{3}{4}(x^2+4x+6)=(13x-2)\\\\Multiply\ both\ sides\ by\ 4.\\\\3(x^2+4x+6)=4(13x-2)\\\\3x^2+12x+18=52x-8\\\\3x^2+12x+18-(52x-8)=0\\\\3x^2+12x-52x+18+8=0\\\\3x^2-40x+26=0$

Roots of Polynomial:

$Roots\ are\ polynomial\ ax^2+bx+c=0\\\\x=\frac{-b\pm \sqrt{(b^2-4ac)}}{2a}$

$Here\ a=3,\ b-40,\ c=26\\\\x=\frac{-(-40)\pm \sqrt{(-40)^2-4\times 3\times 26}}{2\times 3}\\\\x=\frac{40\pm\sqrt{1288}}{6}\\\\x_1=\frac{40+\sqrt{1288}}{6}\approx 12.65\\\\x_2=\frac{40-\sqrt{1288}}{6}\approx 0.685$