49x^2-56x+16=289

Solution for 49x^2-56x+16=289 equation:

49x^2-56x+16=289

We move all terms to the left:

49x^2-56x+16-(289)=0

We add all the numbers together, and all the variables

49x^2-56x-273=0

a = 49; b = -56; c = -273;
Δ = b2-4ac
Δ = -562-4·49·(-273)
Δ = 56644
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{56644}=238$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-238}{2*49}=\frac{-182}{98}
=-1+6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+238}{2*49}=\frac{294}{98}
=3
$