5x^2+15x-35=0

Solution for 5x^2+15x-35=0 equation:

5x^2+15x-35=0

a = 5; b = 15; c = -35;
Δ = b2-4ac
Δ = 152-4·5·(-35)
Δ = 925
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:

$\sqrt{\Delta}=\sqrt{925}=\sqrt{25*37}=\sqrt{25}*\sqrt{37}=5\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{37}}{2*5}=\frac{-15-5\sqrt{37}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{37}}{2*5}=\frac{-15+5\sqrt{37}}{10}
$