4x-5-2x^2=-12x^2-10x-9

Solution for 4x-5-2x^2=-12x^2-10x-9 equation:

4x-5-2x^2=-12x^2-10x-9

We move all terms to the left:

4x-5-2x^2-(-12x^2-10x-9)=0

We get rid of parentheses

-2x^2+12x^2+10x+4x+9-5=0

We add all the numbers together, and all the variables

10x^2+14x+4=0

a = 10; b = 14; c = +4;
Δ = b2-4ac
Δ = 142-4·10·4
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6}{2*10}=\frac{-20}{20}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6}{2*10}=\frac{-8}{20}
=-2/5
$