-7x^2+78x-24=0

Solution for -7x^2+78x-24=0 equation:

-7x^2+78x-24=0

a = -7; b = 78; c = -24;
Δ = b2-4ac
Δ = 782-4·(-7)·(-24)
Δ = 5412
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:

$\sqrt{\Delta}=\sqrt{5412}=\sqrt{4*1353}=\sqrt{4}*\sqrt{1353}=2\sqrt{1353}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{1353}}{2*-7}=\frac{-78-2\sqrt{1353}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{1353}}{2*-7}=\frac{-78+2\sqrt{1353}}{-14}
$