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(7x-19)(17x-19)+(4x+2)(4x+2)=34*34
We move all terms to the left:
(7x-19)(17x-19)+(4x+2)(4x+2)-(34*34)=0
We add all the numbers together, and all the variables
(7x-19)(17x-19)+(4x+2)(4x+2)-1156=0
We multiply parentheses ..
(+119x^2-133x-323x+361)+(4x+2)(4x+2)-1156=0
We get rid of parentheses
119x^2-133x-323x+(4x+2)(4x+2)+361-1156=0
We multiply parentheses ..
119x^2+(+16x^2+8x+8x+4)-133x-323x+361-1156=0
We add all the numbers together, and all the variables
119x^2+(+16x^2+8x+8x+4)-456x-795=0
We get rid of parentheses
119x^2+16x^2+8x+8x-456x+4-795=0
We add all the numbers together, and all the variables
135x^2-440x-791=0
a = 135; b = -440; c = -791;
Δ = b2-4ac
Δ = -4402-4·135·(-791)
Δ = 620740
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{620740}=\sqrt{4*155185}=\sqrt{4}*\sqrt{155185}=2\sqrt{155185}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-440)-2\sqrt{155185}}{2*135}=\frac{440-2\sqrt{155185}}{270} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-440)+2\sqrt{155185}}{2*135}=\frac{440+2\sqrt{155185}}{270} $
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