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7x^2=-3x+18
We move all terms to the left:
7x^2-(-3x+18)=0
We get rid of parentheses
7x^2+3x-18=0
a = 7; b = 3; c = -18;
Δ = b2-4ac
Δ = 32-4·7·(-18)
Δ = 513
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{57}}{2*7}=\frac{-3-3\sqrt{57}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{57}}{2*7}=\frac{-3+3\sqrt{57}}{14} $
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