2(x^2-7x)=-3-6x^2

Solution for 2(x^2-7x)=-3-6x^2 equation:

2(x^2-7x)=-3-6x^2

We move all terms to the left:

2(x^2-7x)-(-3-6x^2)=0

We multiply parentheses

-(-3-6x^2)+2x^2-14x=0

We get rid of parentheses

6x^2+2x^2-14x+3=0

We add all the numbers together, and all the variables

8x^2-14x+3=0

a = 8; b = -14; c = +3;
Δ = b2-4ac
Δ = -142-4·8·3
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-10}{2*8}=\frac{4}{16}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10}{2*8}=\frac{24}{16}
=1+1/2
$