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6x+7=-2x^2+60
We move all terms to the left:
6x+7-(-2x^2+60)=0
We get rid of parentheses
2x^2+6x-60+7=0
We add all the numbers together, and all the variables
2x^2+6x-53=0
a = 2; b = 6; c = -53;
Δ = b2-4ac
Δ = 62-4·2·(-53)
Δ = 460
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{115}}{2*2}=\frac{-6-2\sqrt{115}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{115}}{2*2}=\frac{-6+2\sqrt{115}}{4} $
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