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9x(3x-7)=25
We move all terms to the left:
9x(3x-7)-(25)=0
We multiply parentheses
27x^2-63x-25=0
a = 27; b = -63; c = -25;
Δ = b2-4ac
Δ = -632-4·27·(-25)
Δ = 6669
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6669}=\sqrt{9*741}=\sqrt{9}*\sqrt{741}=3\sqrt{741}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-3\sqrt{741}}{2*27}=\frac{63-3\sqrt{741}}{54} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+3\sqrt{741}}{2*27}=\frac{63+3\sqrt{741}}{54} $
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