X=7x^2-9x+8-2x-13x^2

Solution for X=7x^2-9x+8-2x-13x^2 equation:

X=7X^2-9X+8-2X-13X^2

We move all terms to the left:

X-(7X^2-9X+8-2X-13X^2)=0

We get rid of parentheses

-7X^2+13X^2+9X+2X+X-8=0

We add all the numbers together, and all the variables

6X^2+12X-8=0

a = 6; b = 12; c = -8;
Δ = b2-4ac
Δ = 122-4·6·(-8)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{21}}{2*6}=\frac{-12-4\sqrt{21}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{21}}{2*6}=\frac{-12+4\sqrt{21}}{12}
$