5x2+14x=x+6

Solution for 5x2+14x=x+6 equation:

5x^2+14x=x+6

We move all terms to the left:

5x^2+14x-(x+6)=0

We get rid of parentheses

5x^2+14x-x-6=0

We add all the numbers together, and all the variables

5x^2+13x-6=0

a = 5; b = 13; c = -6;
Δ = b2-4ac
Δ = 132-4·5·(-6)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-17}{2*5}=\frac{-30}{10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+17}{2*5}=\frac{4}{10}
=2/5
$