7x^2=-196+77x

Solution for 7x^2=-196+77x equation:

7x^2=-196+77x

We move all terms to the left:

7x^2-(-196+77x)=0

We add all the numbers together, and all the variables

7x^2-(77x-196)=0

We get rid of parentheses

7x^2-77x+196=0

a = 7; b = -77; c = +196;
Δ = b2-4ac
Δ = -772-4·7·196
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{-(-77)-21}{2*7}=\frac{56}{14}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+21}{2*7}=\frac{98}{14}
=7
$