-x^2+6.5x+42=0

Solution for -x^2+6.5x+42=0 equation:

-x^2+6.5x+42=0

We add all the numbers together, and all the variables

-1x^2+6.5x+42=0

a = -1; b = 6.5; c = +42;
Δ = b2-4ac
Δ = 6.52-4·(-1)·42
Δ = 210.25
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{-(6.5)-\sqrt{210.25}}{2*-1}=\frac{-6.5-\sqrt{210.25}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6.5)+\sqrt{210.25}}{2*-1}=\frac{-6.5+\sqrt{210.25}}{-2}
$