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(4x+6)(x-5)=6
We move all terms to the left:
(4x+6)(x-5)-(6)=0
We multiply parentheses ..
(+4x^2-20x+6x-30)-6=0
We get rid of parentheses
4x^2-20x+6x-30-6=0
We add all the numbers together, and all the variables
4x^2-14x-36=0
a = 4; b = -14; c = -36;
Δ = b2-4ac
Δ = -142-4·4·(-36)
Δ = 772
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{193}}{2*4}=\frac{14-2\sqrt{193}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{193}}{2*4}=\frac{14+2\sqrt{193}}{8} $
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