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3x+7=5x^2-4
We move all terms to the left:
3x+7-(5x^2-4)=0
We get rid of parentheses
-5x^2+3x+4+7=0
We add all the numbers together, and all the variables
-5x^2+3x+11=0
a = -5; b = 3; c = +11;
Δ = b2-4ac
Δ = 32-4·(-5)·11
Δ = 229
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{229}}{2*-5}=\frac{-3-\sqrt{229}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{229}}{2*-5}=\frac{-3+\sqrt{229}}{-10} $
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