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6x(3x-5)=22
We move all terms to the left:
6x(3x-5)-(22)=0
We multiply parentheses
18x^2-30x-22=0
a = 18; b = -30; c = -22;
Δ = b2-4ac
Δ = -302-4·18·(-22)
Δ = 2484
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2484}=\sqrt{36*69}=\sqrt{36}*\sqrt{69}=6\sqrt{69}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{69}}{2*18}=\frac{30-6\sqrt{69}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{69}}{2*18}=\frac{30+6\sqrt{69}}{36} $
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