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x(4x-30)=180
We move all terms to the left:
x(4x-30)-(180)=0
We multiply parentheses
4x^2-30x-180=0
a = 4; b = -30; c = -180;
Δ = b2-4ac
Δ = -302-4·4·(-180)
Δ = 3780
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3780}=\sqrt{36*105}=\sqrt{36}*\sqrt{105}=6\sqrt{105}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{105}}{2*4}=\frac{30-6\sqrt{105}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{105}}{2*4}=\frac{30+6\sqrt{105}}{8} $
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