21x^2=77x-28

Solution for 21x^2=77x-28 equation:

21x^2=77x-28

We move all terms to the left:

21x^2-(77x-28)=0

We get rid of parentheses

21x^2-77x+28=0

a = 21; b = -77; c = +28;
Δ = b2-4ac
Δ = -772-4·21·28
Δ = 3577
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3577}=\sqrt{49*73}=\sqrt{49}*\sqrt{73}=7\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-7\sqrt{73}}{2*21}=\frac{77-7\sqrt{73}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+7\sqrt{73}}{2*21}=\frac{77+7\sqrt{73}}{42}
$