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135+45x=2.6x^2
We move all terms to the left:
135+45x-(2.6x^2)=0
We get rid of parentheses
-2.6x^2+45x+135=0
a = -2.6; b = 45; c = +135;
Δ = b2-4ac
Δ = 452-4·(-2.6)·135
Δ = 3429
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3429}=\sqrt{9*381}=\sqrt{9}*\sqrt{381}=3\sqrt{381}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{381}}{2*-2.6}=\frac{-45-3\sqrt{381}}{-5.2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{381}}{2*-2.6}=\frac{-45+3\sqrt{381}}{-5.2} $
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