5x(x-1)=-7x^2+2

Solution for 5x(x-1)=-7x^2+2 equation:

5x(x-1)=-7x^2+2

We move all terms to the left:

5x(x-1)-(-7x^2+2)=0

We multiply parentheses

-(-7x^2+2)+5x^2-5x=0

We get rid of parentheses

7x^2+5x^2-5x-2=0

We add all the numbers together, and all the variables

12x^2-5x-2=0

a = 12; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·12·(-2)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*12}=\frac{-6}{24}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*12}=\frac{16}{24}
=2/3
$