-10x^2=-7x+1

Solution for -10x^2=-7x+1 equation:

-10x^2=-7x+1

We move all terms to the left:

-10x^2-(-7x+1)=0

We get rid of parentheses

-10x^2+7x-1=0

a = -10; b = 7; c = -1;
Δ = b2-4ac
Δ = 72-4·(-10)·(-1)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3}{2*-10}=\frac{-10}{-20}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3}{2*-10}=\frac{-4}{-20}
=1/5
$