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(6x-4)(4x+14)=90
We move all terms to the left:
(6x-4)(4x+14)-(90)=0
We multiply parentheses ..
(+24x^2+84x-16x-56)-90=0
We get rid of parentheses
24x^2+84x-16x-56-90=0
We add all the numbers together, and all the variables
24x^2+68x-146=0
a = 24; b = 68; c = -146;
Δ = b2-4ac
Δ = 682-4·24·(-146)
Δ = 18640
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{18640}=\sqrt{16*1165}=\sqrt{16}*\sqrt{1165}=4\sqrt{1165}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-4\sqrt{1165}}{2*24}=\frac{-68-4\sqrt{1165}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+4\sqrt{1165}}{2*24}=\frac{-68+4\sqrt{1165}}{48} $
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