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(3t+5)-(4t+8)(7t-3)=4
We move all terms to the left:
(3t+5)-(4t+8)(7t-3)-(4)=0
We get rid of parentheses
3t-(4t+8)(7t-3)+5-4=0
We multiply parentheses ..
-(+28t^2-12t+56t-24)+3t+5-4=0
We add all the numbers together, and all the variables
-(+28t^2-12t+56t-24)+3t+1=0
We get rid of parentheses
-28t^2+12t-56t+3t+24+1=0
We add all the numbers together, and all the variables
-28t^2-41t+25=0
a = -28; b = -41; c = +25;
Δ = b2-4ac
Δ = -412-4·(-28)·25
Δ = 4481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-\sqrt{4481}}{2*-28}=\frac{41-\sqrt{4481}}{-56} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{4481}}{2*-28}=\frac{41+\sqrt{4481}}{-56} $
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