x^2+1.5x+0.5625=3.0625

Solution for x^2+1.5x+0.5625=3.0625 equation:

x^2+1.5x+0.5625=3.0625

We move all terms to the left:

x^2+1.5x+0.5625-(3.0625)=0

We add all the numbers together, and all the variables

x^2+1.5x-2.5=0

a = 1; b = 1.5; c = -2.5;
Δ = b2-4ac
Δ = 1.52-4·1·(-2.5)
Δ = 12.25
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{-(1.5)-\sqrt{12.25}}{2*1}=\frac{-1.5-\sqrt{12.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{12.25}}{2*1}=\frac{-1.5+\sqrt{12.25}}{2}
$