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7x^2-135x+288=0
a = 7; b = -135; c = +288;
Δ = b2-4ac
Δ = -1352-4·7·288
Δ = 10161
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10161}=\sqrt{9*1129}=\sqrt{9}*\sqrt{1129}=3\sqrt{1129}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-3\sqrt{1129}}{2*7}=\frac{135-3\sqrt{1129}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+3\sqrt{1129}}{2*7}=\frac{135+3\sqrt{1129}}{14} $
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