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5x^2-2+x=8x+3
We move all terms to the left:
5x^2-2+x-(8x+3)=0
We get rid of parentheses
5x^2+x-8x-3-2=0
We add all the numbers together, and all the variables
5x^2-7x-5=0
a = 5; b = -7; c = -5;
Δ = b2-4ac
Δ = -72-4·5·(-5)
Δ = 149
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{-(-7)-\sqrt{149}}{2*5}=\frac{7-\sqrt{149}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{149}}{2*5}=\frac{7+\sqrt{149}}{10} $
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