7x^2-15x-275=0

Solution for 7x^2-15x-275=0 equation:

7x^2-15x-275=0

a = 7; b = -15; c = -275;
Δ = b2-4ac
Δ = -152-4·7·(-275)
Δ = 7925
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:

$\sqrt{\Delta}=\sqrt{7925}=\sqrt{25*317}=\sqrt{25}*\sqrt{317}=5\sqrt{317}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{317}}{2*7}=\frac{15-5\sqrt{317}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{317}}{2*7}=\frac{15+5\sqrt{317}}{14}
$