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(7x+2)(5x+4)=90
We move all terms to the left:
(7x+2)(5x+4)-(90)=0
We multiply parentheses ..
(+35x^2+28x+10x+8)-90=0
We get rid of parentheses
35x^2+28x+10x+8-90=0
We add all the numbers together, and all the variables
35x^2+38x-82=0
a = 35; b = 38; c = -82;
Δ = b2-4ac
Δ = 382-4·35·(-82)
Δ = 12924
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12924}=\sqrt{36*359}=\sqrt{36}*\sqrt{359}=6\sqrt{359}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-6\sqrt{359}}{2*35}=\frac{-38-6\sqrt{359}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+6\sqrt{359}}{2*35}=\frac{-38+6\sqrt{359}}{70} $
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