7x^2=49x+56

Solution for 7x^2=49x+56 equation:

7x^2=49x+56

We move all terms to the left:

7x^2-(49x+56)=0

We get rid of parentheses

7x^2-49x-56=0

a = 7; b = -49; c = -56;
Δ = b2-4ac
Δ = -492-4·7·(-56)
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-63}{2*7}=\frac{-14}{14}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+63}{2*7}=\frac{112}{14}
=8
$