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(2x+7)(4x-7)=90
We move all terms to the left:
(2x+7)(4x-7)-(90)=0
We multiply parentheses ..
(+8x^2-14x+28x-49)-90=0
We get rid of parentheses
8x^2-14x+28x-49-90=0
We add all the numbers together, and all the variables
8x^2+14x-139=0
a = 8; b = 14; c = -139;
Δ = b2-4ac
Δ = 142-4·8·(-139)
Δ = 4644
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4644}=\sqrt{36*129}=\sqrt{36}*\sqrt{129}=6\sqrt{129}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6\sqrt{129}}{2*8}=\frac{-14-6\sqrt{129}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6\sqrt{129}}{2*8}=\frac{-14+6\sqrt{129}}{16} $
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