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(5x-15)(3x+1)=58
We move all terms to the left:
(5x-15)(3x+1)-(58)=0
We multiply parentheses ..
(+15x^2+5x-45x-15)-58=0
We get rid of parentheses
15x^2+5x-45x-15-58=0
We add all the numbers together, and all the variables
15x^2-40x-73=0
a = 15; b = -40; c = -73;
Δ = b2-4ac
Δ = -402-4·15·(-73)
Δ = 5980
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5980}=\sqrt{4*1495}=\sqrt{4}*\sqrt{1495}=2\sqrt{1495}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{1495}}{2*15}=\frac{40-2\sqrt{1495}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{1495}}{2*15}=\frac{40+2\sqrt{1495}}{30} $
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