30x^2-10x-2=-5x^2+12x-5

Solution for 30x^2-10x-2=-5x^2+12x-5 equation:

30x^2-10x-2=-5x^2+12x-5

We move all terms to the left:

30x^2-10x-2-(-5x^2+12x-5)=0

We get rid of parentheses

30x^2+5x^2-12x-10x+5-2=0

We add all the numbers together, and all the variables

35x^2-22x+3=0

a = 35; b = -22; c = +3;
Δ = b2-4ac
Δ = -222-4·35·3
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-8}{2*35}=\frac{14}{70}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+8}{2*35}=\frac{30}{70}
=3/7
$