14x+7=3x^2-1x

Solution for 14x+7=3x^2-1x equation:

14x+7=3x^2-1x

We move all terms to the left:

14x+7-(3x^2-1x)=0

We get rid of parentheses

-3x^2+14x+1x+7=0

We add all the numbers together, and all the variables

-3x^2+15x+7=0

a = -3; b = 15; c = +7;
Δ = b2-4ac
Δ = 152-4·(-3)·7
Δ = 309
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{-(15)-\sqrt{309}}{2*-3}=\frac{-15-\sqrt{309}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{309}}{2*-3}=\frac{-15+\sqrt{309}}{-6}
$