5x^2-49=5x+51

Solution for 5x^2-49=5x+51 equation:

5x^2-49=5x+51

We move all terms to the left:

5x^2-49-(5x+51)=0

We get rid of parentheses

5x^2-5x-51-49=0

We add all the numbers together, and all the variables

5x^2-5x-100=0

a = 5; b = -5; c = -100;
Δ = b2-4ac
Δ = -52-4·5·(-100)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-45}{2*5}=\frac{-40}{10}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+45}{2*5}=\frac{50}{10}
=5
$