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(6x-25)(4x+15)=180
We move all terms to the left:
(6x-25)(4x+15)-(180)=0
We multiply parentheses ..
(+24x^2+90x-100x-375)-180=0
We get rid of parentheses
24x^2+90x-100x-375-180=0
We add all the numbers together, and all the variables
24x^2-10x-555=0
a = 24; b = -10; c = -555;
Δ = b2-4ac
Δ = -102-4·24·(-555)
Δ = 53380
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{53380}=\sqrt{4*13345}=\sqrt{4}*\sqrt{13345}=2\sqrt{13345}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{13345}}{2*24}=\frac{10-2\sqrt{13345}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{13345}}{2*24}=\frac{10+2\sqrt{13345}}{48} $
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