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(5+3x)(7-x)=04
We move all terms to the left:
(5+3x)(7-x)-(04)=0
We add all the numbers together, and all the variables
(3x+5)(-1x+7)-04=0
We add all the numbers together, and all the variables
(3x+5)(-1x+7)-4=0
We multiply parentheses ..
(-3x^2+21x-5x+35)-4=0
We get rid of parentheses
-3x^2+21x-5x+35-4=0
We add all the numbers together, and all the variables
-3x^2+16x+31=0
a = -3; b = 16; c = +31;
Δ = b2-4ac
Δ = 162-4·(-3)·31
Δ = 628
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{157}}{2*-3}=\frac{-16-2\sqrt{157}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{157}}{2*-3}=\frac{-16+2\sqrt{157}}{-6} $
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