8x^2+10x-54=0

Solution for 8x^2+10x-54=0 equation:

8x^2+10x-54=0

a = 8; b = 10; c = -54;
Δ = b2-4ac
Δ = 102-4·8·(-54)
Δ = 1828
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:

$\sqrt{\Delta}=\sqrt{1828}=\sqrt{4*457}=\sqrt{4}*\sqrt{457}=2\sqrt{457}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{457}}{2*8}=\frac{-10-2\sqrt{457}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{457}}{2*8}=\frac{-10+2\sqrt{457}}{16}
$