X^2-3x+10/12=2x^2-2x+8/12

Solution for X^2-3x+10/12=2x^2-2x+8/12 equation:

X^2-3X+10/12=2X^2-2X+8/12

We move all terms to the left:

X^2-3X+10/12-(2X^2-2X+8/12)=0

We get rid of parentheses

X^2-2X^2-3X+2X-8/12+10/12=0

We multiply all the terms by the denominator


X^2*12-2X^2*12-3X*12+2X*12-8+10=0

We add all the numbers together, and all the variables

X^2*12-2X^2*12-3X*12+2X*12+2=0

Wy multiply elements

12X^2-24X^2-36X+24X+2=0

We add all the numbers together, and all the variables

-12X^2-12X+2=0

a = -12; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·(-12)·2
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{15}}{2*-12}=\frac{12-4\sqrt{15}}{-24}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{15}}{2*-12}=\frac{12+4\sqrt{15}}{-24}
$