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(x+5)(4x+1)=15
We move all terms to the left:
(x+5)(4x+1)-(15)=0
We multiply parentheses ..
(+4x^2+x+20x+5)-15=0
We get rid of parentheses
4x^2+x+20x+5-15=0
We add all the numbers together, and all the variables
4x^2+21x-10=0
a = 4; b = 21; c = -10;
Δ = b2-4ac
Δ = 212-4·4·(-10)
Δ = 601
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{-(21)-\sqrt{601}}{2*4}=\frac{-21-\sqrt{601}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{601}}{2*4}=\frac{-21+\sqrt{601}}{8} $
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