-4a^2+148a-240=0

Solution for -4a^2+148a-240=0 equation:

-4a^2+148a-240=0

a = -4; b = 148; c = -240;
Δ = b2-4ac
Δ = 1482-4·(-4)·(-240)
Δ = 18064
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{18064}=\sqrt{16*1129}=\sqrt{16}*\sqrt{1129}=4\sqrt{1129}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(148)-4\sqrt{1129}}{2*-4}=\frac{-148-4\sqrt{1129}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(148)+4\sqrt{1129}}{2*-4}=\frac{-148+4\sqrt{1129}}{-8}
$