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(5x+7)2=17x^2+84x+46
We move all terms to the left:
(5x+7)2-(17x^2+84x+46)=0
We multiply parentheses
10x-(17x^2+84x+46)+14=0
We get rid of parentheses
-17x^2+10x-84x-46+14=0
We add all the numbers together, and all the variables
-17x^2-74x-32=0
a = -17; b = -74; c = -32;
Δ = b2-4ac
Δ = -742-4·(-17)·(-32)
Δ = 3300
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3300}=\sqrt{100*33}=\sqrt{100}*\sqrt{33}=10\sqrt{33}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-10\sqrt{33}}{2*-17}=\frac{74-10\sqrt{33}}{-34} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+10\sqrt{33}}{2*-17}=\frac{74+10\sqrt{33}}{-34} $
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