5x^2+14x=x+5

Solution for 5x^2+14x=x+5 equation:

5x^2+14x=x+5

We move all terms to the left:

5x^2+14x-(x+5)=0

We get rid of parentheses

5x^2+14x-x-5=0

We add all the numbers together, and all the variables

5x^2+13x-5=0

a = 5; b = 13; c = -5;
Δ = b2-4ac
Δ = 132-4·5·(-5)
Δ = 269
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{269}}{2*5}=\frac{-13-\sqrt{269}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{269}}{2*5}=\frac{-13+\sqrt{269}}{10}
$