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49x^2-15x-90=0
a = 49; b = -15; c = -90;
Δ = b2-4ac
Δ = -152-4·49·(-90)
Δ = 17865
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{17865}=\sqrt{9*1985}=\sqrt{9}*\sqrt{1985}=3\sqrt{1985}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{1985}}{2*49}=\frac{15-3\sqrt{1985}}{98} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{1985}}{2*49}=\frac{15+3\sqrt{1985}}{98} $
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