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4x^2-61x+25=0
a = 4; b = -61; c = +25;
Δ = b2-4ac
Δ = -612-4·4·25
Δ = 3321
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3321}=\sqrt{81*41}=\sqrt{81}*\sqrt{41}=9\sqrt{41}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-61)-9\sqrt{41}}{2*4}=\frac{61-9\sqrt{41}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+9\sqrt{41}}{2*4}=\frac{61+9\sqrt{41}}{8} $
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