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(4x+7)(5x+2)=90
We move all terms to the left:
(4x+7)(5x+2)-(90)=0
We multiply parentheses ..
(+20x^2+8x+35x+14)-90=0
We get rid of parentheses
20x^2+8x+35x+14-90=0
We add all the numbers together, and all the variables
20x^2+43x-76=0
a = 20; b = 43; c = -76;
Δ = b2-4ac
Δ = 432-4·20·(-76)
Δ = 7929
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7929}=\sqrt{9*881}=\sqrt{9}*\sqrt{881}=3\sqrt{881}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-3\sqrt{881}}{2*20}=\frac{-43-3\sqrt{881}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+3\sqrt{881}}{2*20}=\frac{-43+3\sqrt{881}}{40} $
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