7x^2=14x-56/9

Solution for 7x^2=14x-56/9 equation:

7x^2=14x-56/9

We move all terms to the left:

7x^2-(14x-56/9)=0

We add all the numbers together, and all the variables

7x^2-(+14x-56/9)=0

We get rid of parentheses

7x^2-14x+56/9=0

We multiply all the terms by the denominator


7x^2*9-14x*9+56=0

Wy multiply elements

63x^2-126x+56=0

a = 63; b = -126; c = +56;
Δ = b2-4ac
Δ = -1262-4·63·56
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-42}{2*63}=\frac{84}{126}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+42}{2*63}=\frac{168}{126}
=1+1/3
$