0.52(x^2-0.545x+0.0225)=x^2+0.090x+0.0020

Solution for 0.52(x^2-0.545x+0.0225)=x^2+0.090x+0.0020 equation:

0.52(x^2-0.545x+0.0225)=x^2+0.090x+0.0020

We move all terms to the left:

0.52(x^2-0.545x+0.0225)-(x^2+0.090x+0.0020)=0

We multiply parentheses

0.52x^2+0x-(x^2+0.090x+0.0020)+0.0117=0

We get rid of parentheses

0.52x^2-x^2+0x-0.090x-0.0020+0.0117=0

We add all the numbers together, and all the variables

-0.48x^2+0.91x+0.0097=0

a = -0.48; b = 0.91; c = +0.0097;
Δ = b2-4ac
Δ = 0.912-4·(-0.48)·0.0097
Δ = 0.846724
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{-(0.91)-\sqrt{0.846724}}{2*-0.48}=\frac{-0.91-\sqrt{0.846724}}{-0.96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.91)+\sqrt{0.846724}}{2*-0.48}=\frac{-0.91+\sqrt{0.846724}}{-0.96}
$