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(5x+2)(3x-2)=60
We move all terms to the left:
(5x+2)(3x-2)-(60)=0
We multiply parentheses ..
(+15x^2-10x+6x-4)-60=0
We get rid of parentheses
15x^2-10x+6x-4-60=0
We add all the numbers together, and all the variables
15x^2-4x-64=0
a = 15; b = -4; c = -64;
Δ = b2-4ac
Δ = -42-4·15·(-64)
Δ = 3856
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3856}=\sqrt{16*241}=\sqrt{16}*\sqrt{241}=4\sqrt{241}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{241}}{2*15}=\frac{4-4\sqrt{241}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{241}}{2*15}=\frac{4+4\sqrt{241}}{30} $
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