12x^2-3=-10x

Solution for 12x^2-3=-10x equation:

12x^2-3=-10x

We move all terms to the left:

12x^2-3-(-10x)=0

We get rid of parentheses

12x^2+10x-3=0

a = 12; b = 10; c = -3;
Δ = b2-4ac
Δ = 102-4·12·(-3)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{61}}{2*12}=\frac{-10-2\sqrt{61}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{61}}{2*12}=\frac{-10+2\sqrt{61}}{24}
$