10x^2-20x-6=-5x^2+7x

Solution for 10x^2-20x-6=-5x^2+7x equation:

10x^2-20x-6=-5x^2+7x

We move all terms to the left:

10x^2-20x-6-(-5x^2+7x)=0

We get rid of parentheses

10x^2+5x^2-7x-20x-6=0

We add all the numbers together, and all the variables

15x^2-27x-6=0

a = 15; b = -27; c = -6;
Δ = b2-4ac
Δ = -272-4·15·(-6)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-33}{2*15}=\frac{-6}{30}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+33}{2*15}=\frac{60}{30}
=2
$