10x-2x^2=-12

Solution for 10x-2x^2=-12 equation:

10x-2x^2=-12

We move all terms to the left:

10x-2x^2-(-12)=0

We add all the numbers together, and all the variables

-2x^2+10x+12=0

a = -2; b = 10; c = +12;
Δ = b2-4ac
Δ = 102-4·(-2)·12
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*-2}=\frac{-24}{-4}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*-2}=\frac{4}{-4}
=-1
$