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(2x+7)(8x-2)=65
We move all terms to the left:
(2x+7)(8x-2)-(65)=0
We multiply parentheses ..
(+16x^2-4x+56x-14)-65=0
We get rid of parentheses
16x^2-4x+56x-14-65=0
We add all the numbers together, and all the variables
16x^2+52x-79=0
a = 16; b = 52; c = -79;
Δ = b2-4ac
Δ = 522-4·16·(-79)
Δ = 7760
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7760}=\sqrt{16*485}=\sqrt{16}*\sqrt{485}=4\sqrt{485}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{485}}{2*16}=\frac{-52-4\sqrt{485}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{485}}{2*16}=\frac{-52+4\sqrt{485}}{32} $
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