-7+12x=-10x^2

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

-7+12x=-10x^2

We move all terms to the left:

-7+12x-(-10x^2)=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}
$