X2+6.5x=42

Solution for X2+6.5x=42 equation:

X2+6.5X=42

We move all terms to the left:

X2+6.5X-(42)=0

We add all the numbers together, and all the variables

X^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}
$