x^2+2.5x+1.5625=6.5625

Solution for x^2+2.5x+1.5625=6.5625 equation:

x^2+2.5x+1.5625=6.5625

We move all terms to the left:

x^2+2.5x+1.5625-(6.5625)=0

We add all the numbers together, and all the variables

x^2+2.5x-5=0

a = 1; b = 2.5; c = -5;
Δ = b2-4ac
Δ = 2.52-4·1·(-5)
Δ = 26.25
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{-(2.5)-\sqrt{26.25}}{2*1}=\frac{-2.5-\sqrt{26.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{26.25}}{2*1}=\frac{-2.5+\sqrt{26.25}}{2}
$