x^2=6.5x+42

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

x^2=6.5x+42

We move all terms to the left:

x^2-(6.5x+42)=0

We get rid of parentheses

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}
$