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(5x+3)(x-2)=8
We move all terms to the left:
(5x+3)(x-2)-(8)=0
We multiply parentheses ..
(+5x^2-10x+3x-6)-8=0
We get rid of parentheses
5x^2-10x+3x-6-8=0
We add all the numbers together, and all the variables
5x^2-7x-14=0
a = 5; b = -7; c = -14;
Δ = b2-4ac
Δ = -72-4·5·(-14)
Δ = 329
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{329}}{2*5}=\frac{7-\sqrt{329}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{329}}{2*5}=\frac{7+\sqrt{329}}{10} $
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