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(2x-3)(x-5)=180

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Solution for (2x-3)(x-5)=180 equation:



(2x-3)(x-5)=180
We move all terms to the left:
(2x-3)(x-5)-(180)=0
We multiply parentheses ..
(+2x^2-10x-3x+15)-180=0
We get rid of parentheses
2x^2-10x-3x+15-180=0
We add all the numbers together, and all the variables
2x^2-13x-165=0
a = 2; b = -13; c = -165;
Δ = b2-4ac
Δ = -132-4·2·(-165)
Δ = 1489
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{-(-13)-\sqrt{1489}}{2*2}=\frac{13-\sqrt{1489}}{4}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{1489}}{2*2}=\frac{13+\sqrt{1489}}{4}

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