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5x^*45+45=0+45.5x^2+0=0+45.
We move all terms to the left:
5x^*45+45-(0+45.5x^2+0)=0
Wy multiply elements
-(0+45.5x^2+0)+225x+45=0
We get rid of parentheses
-45.5x^2+225x-0-0+45=0
We add all the numbers together, and all the variables
-45.5x^2+225x+45=0
a = -45.5; b = 225; c = +45;
Δ = b2-4ac
Δ = 2252-4·(-45.5)·45
Δ = 58815
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{58815}=\sqrt{9*6535}=\sqrt{9}*\sqrt{6535}=3\sqrt{6535}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(225)-3\sqrt{6535}}{2*-45.5}=\frac{-225-3\sqrt{6535}}{-91} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(225)+3\sqrt{6535}}{2*-45.5}=\frac{-225+3\sqrt{6535}}{-91} $
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