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(2x+5)(4x+3)=180
We move all terms to the left:
(2x+5)(4x+3)-(180)=0
We multiply parentheses ..
(+8x^2+6x+20x+15)-180=0
We get rid of parentheses
8x^2+6x+20x+15-180=0
We add all the numbers together, and all the variables
8x^2+26x-165=0
a = 8; b = 26; c = -165;
Δ = b2-4ac
Δ = 262-4·8·(-165)
Δ = 5956
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5956}=\sqrt{4*1489}=\sqrt{4}*\sqrt{1489}=2\sqrt{1489}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{1489}}{2*8}=\frac{-26-2\sqrt{1489}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{1489}}{2*8}=\frac{-26+2\sqrt{1489}}{16} $
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