8x^2-55x=42=0

Solution for 8x^2-55x=42=0 equation:

8x^2-55x=42=0

We move all terms to the left:

8x^2-55x-(42)=0

a = 8; b = -55; c = -42;
Δ = b2-4ac
Δ = -552-4·8·(-42)
Δ = 4369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-\sqrt{4369}}{2*8}=\frac{55-\sqrt{4369}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{4369}}{2*8}=\frac{55+\sqrt{4369}}{16}
$