7x^2+20x+21=-x^2+53x+56

Solution for 7x^2+20x+21=-x^2+53x+56 equation:

7x^2+20x+21=-x^2+53x+56

We move all terms to the left:

7x^2+20x+21-(-x^2+53x+56)=0

We get rid of parentheses

7x^2+x^2-53x+20x-56+21=0

We add all the numbers together, and all the variables

8x^2-33x-35=0

a = 8; b = -33; c = -35;
Δ = b2-4ac
Δ = -332-4·8·(-35)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-47}{2*8}=\frac{-14}{16}
=-7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+47}{2*8}=\frac{80}{16}
=5
$