7x^2+15x-2=34

Solution for 7x^2+15x-2=34 equation:

7x^2+15x-2=34

We move all terms to the left:

7x^2+15x-2-(34)=0

We add all the numbers together, and all the variables

7x^2+15x-36=0

a = 7; b = 15; c = -36;
Δ = b2-4ac
Δ = 152-4·7·(-36)
Δ = 1233
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1233}=\sqrt{9*137}=\sqrt{9}*\sqrt{137}=3\sqrt{137}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{137}}{2*7}=\frac{-15-3\sqrt{137}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{137}}{2*7}=\frac{-15+3\sqrt{137}}{14}
$