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49x^2-156x+91=0
a = 49; b = -156; c = +91;
Δ = b2-4ac
Δ = -1562-4·49·91
Δ = 6500
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6500}=\sqrt{100*65}=\sqrt{100}*\sqrt{65}=10\sqrt{65}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-10\sqrt{65}}{2*49}=\frac{156-10\sqrt{65}}{98} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+10\sqrt{65}}{2*49}=\frac{156+10\sqrt{65}}{98} $
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