7x^2=35x-28

Solution for 7x^2=35x-28 equation:

7x^2=35x-28

We move all terms to the left:

7x^2-(35x-28)=0

We get rid of parentheses

7x^2-35x+28=0

a = 7; b = -35; c = +28;
Δ = b2-4ac
Δ = -352-4·7·28
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-21}{2*7}=\frac{14}{14}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+21}{2*7}=\frac{56}{14}
=4
$