2x^2+13x-14=7

Solution for 2x^2+13x-14=7 equation:

2x^2+13x-14=7

We move all terms to the left:

2x^2+13x-14-(7)=0

We add all the numbers together, and all the variables

2x^2+13x-21=0

a = 2; b = 13; c = -21;
Δ = b2-4ac
Δ = 132-4·2·(-21)
Δ = 337
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{337}}{2*2}=\frac{-13-\sqrt{337}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{337}}{2*2}=\frac{-13+\sqrt{337}}{4}
$