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(5+2x)(4x+1)=180
We move all terms to the left:
(5+2x)(4x+1)-(180)=0
We add all the numbers together, and all the variables
(2x+5)(4x+1)-180=0
We multiply parentheses ..
(+8x^2+2x+20x+5)-180=0
We get rid of parentheses
8x^2+2x+20x+5-180=0
We add all the numbers together, and all the variables
8x^2+22x-175=0
a = 8; b = 22; c = -175;
Δ = b2-4ac
Δ = 222-4·8·(-175)
Δ = 6084
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{6084}=78$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-78}{2*8}=\frac{-100}{16} =-6+1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+78}{2*8}=\frac{56}{16} =3+1/2 $
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