-7x^2+4x=-3

Solution for -7x^2+4x=-3 equation:

-7x^2+4x=-3

We move all terms to the left:

-7x^2+4x-(-3)=0

We add all the numbers together, and all the variables

-7x^2+4x+3=0

a = -7; b = 4; c = +3;
Δ = b2-4ac
Δ = 42-4·(-7)·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{-(4)-10}{2*-7}=\frac{-14}{-14}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+10}{2*-7}=\frac{6}{-14}
=-3/7
$