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23x^2-130x+125=0
a = 23; b = -130; c = +125;
Δ = b2-4ac
Δ = -1302-4·23·125
Δ = 5400
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5400}=\sqrt{900*6}=\sqrt{900}*\sqrt{6}=30\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-30\sqrt{6}}{2*23}=\frac{130-30\sqrt{6}}{46} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+30\sqrt{6}}{2*23}=\frac{130+30\sqrt{6}}{46} $
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