5x^2+78x-53=0

Solution for 5x^2+78x-53=0 equation:

5x^2+78x-53=0

a = 5; b = 78; c = -53;
Δ = b2-4ac
Δ = 782-4·5·(-53)
Δ = 7144
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:

$\sqrt{\Delta}=\sqrt{7144}=\sqrt{4*1786}=\sqrt{4}*\sqrt{1786}=2\sqrt{1786}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{1786}}{2*5}=\frac{-78-2\sqrt{1786}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{1786}}{2*5}=\frac{-78+2\sqrt{1786}}{10}
$