x=310x2-7x-12

Solution for x=310x2-7x-12 equation:

x=310x^2-7x-12

We move all terms to the left:

x-(310x^2-7x-12)=0

We get rid of parentheses

-310x^2+x+7x+12=0

We add all the numbers together, and all the variables

-310x^2+8x+12=0

a = -310; b = 8; c = +12;
Δ = b2-4ac
Δ = 82-4·(-310)·12
Δ = 14944
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:

$\sqrt{\Delta}=\sqrt{14944}=\sqrt{16*934}=\sqrt{16}*\sqrt{934}=4\sqrt{934}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{934}}{2*-310}=\frac{-8-4\sqrt{934}}{-620}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{934}}{2*-310}=\frac{-8+4\sqrt{934}}{-620}
$