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2x^2=30x+180
We move all terms to the left:
2x^2-(30x+180)=0
We get rid of parentheses
2x^2-30x-180=0
a = 2; b = -30; c = -180;
Δ = b2-4ac
Δ = -302-4·2·(-180)
Δ = 2340
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{65}}{2*2}=\frac{30-6\sqrt{65}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{65}}{2*2}=\frac{30+6\sqrt{65}}{4} $
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