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5x+7=-14+8x^2
We move all terms to the left:
5x+7-(-14+8x^2)=0
We get rid of parentheses
-8x^2+5x+14+7=0
We add all the numbers together, and all the variables
-8x^2+5x+21=0
a = -8; b = 5; c = +21;
Δ = b2-4ac
Δ = 52-4·(-8)·21
Δ = 697
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{-(5)-\sqrt{697}}{2*-8}=\frac{-5-\sqrt{697}}{-16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{697}}{2*-8}=\frac{-5+\sqrt{697}}{-16} $
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