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3x*5x+4=2500
We move all terms to the left:
3x*5x+4-(2500)=0
We add all the numbers together, and all the variables
3x*5x-2496=0
Wy multiply elements
15x^2-2496=0
a = 15; b = 0; c = -2496;
Δ = b2-4ac
Δ = 02-4·15·(-2496)
Δ = 149760
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{149760}=\sqrt{2304*65}=\sqrt{2304}*\sqrt{65}=48\sqrt{65}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{65}}{2*15}=\frac{0-48\sqrt{65}}{30} =-\frac{48\sqrt{65}}{30} =-\frac{8\sqrt{65}}{5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{65}}{2*15}=\frac{0+48\sqrt{65}}{30} =\frac{48\sqrt{65}}{30} =\frac{8\sqrt{65}}{5} $
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