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9x(5x-2)=-12+45x
We move all terms to the left:
9x(5x-2)-(-12+45x)=0
We add all the numbers together, and all the variables
9x(5x-2)-(45x-12)=0
We multiply parentheses
45x^2-18x-(45x-12)=0
We get rid of parentheses
45x^2-18x-45x+12=0
We add all the numbers together, and all the variables
45x^2-63x+12=0
a = 45; b = -63; c = +12;
Δ = b2-4ac
Δ = -632-4·45·12
Δ = 1809
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1809}=\sqrt{9*201}=\sqrt{9}*\sqrt{201}=3\sqrt{201}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-3\sqrt{201}}{2*45}=\frac{63-3\sqrt{201}}{90} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+3\sqrt{201}}{2*45}=\frac{63+3\sqrt{201}}{90} $
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