-5x^2-7x+34=0

Solution for -5x^2-7x+34=0 equation:

-5x^2-7x+34=0

a = -5; b = -7; c = +34;
Δ = b2-4ac
Δ = -72-4·(-5)·34
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-27}{2*-5}=\frac{-20}{-10}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+27}{2*-5}=\frac{34}{-10}
=-3+2/5
$