5x^2-12x-5=-3x

Solution for 5x^2-12x-5=-3x equation:

5x^2-12x-5=-3x

We move all terms to the left:

5x^2-12x-5-(-3x)=0

We get rid of parentheses

5x^2-12x+3x-5=0

We add all the numbers together, and all the variables

5x^2-9x-5=0

a = 5; b = -9; c = -5;
Δ = b2-4ac
Δ = -92-4·5·(-5)
Δ = 181
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{181}}{2*5}=\frac{9-\sqrt{181}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{181}}{2*5}=\frac{9+\sqrt{181}}{10}
$