-10x^2=-7+12x

Solution for -10x^2=-7+12x equation:

-10x^2=-7+12x

We move all terms to the left:

-10x^2-(-7+12x)=0

We add all the numbers together, and all the variables

-10x^2-(12x-7)=0

We get rid of parentheses

-10x^2-12x+7=0

a = -10; b = -12; c = +7;
Δ = b2-4ac
Δ = -122-4·(-10)·7
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{106}}{2*-10}=\frac{12-2\sqrt{106}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{106}}{2*-10}=\frac{12+2\sqrt{106}}{-20}
$