(1/4)(16t+36)=-8t-13

Solution for (1/4)(16t+36)=-8t-13 equation:

(1/4)(16t+36)=-8t-13

We move all terms to the left:

(1/4)(16t+36)-(-8t-13)=0


Domain of the equation: 4)(16t+36)!=0

t∈R


We add all the numbers together, and all the variables

(+1/4)(16t+36)-(-8t-13)=0

We get rid of parentheses

(+1/4)(16t+36)+8t+13=0

We multiply parentheses ..

(+16t^2+1/4*36)+8t+13=0

We multiply all the terms by the denominator


(+16t^2+1+8t*4*36)+13*4*36)=0

We add all the numbers together, and all the variables

(+16t^2+1+8t*4*36)=0

We get rid of parentheses

16t^2+8t*4*36+1=0

Wy multiply elements

16t^2+1152t*3+1=0

Wy multiply elements

16t^2+3456t+1=0

a = 16; b = 3456; c = +1;
Δ = b2-4ac
Δ = 34562-4·16·1
Δ = 11943872
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{11943872}=\sqrt{64*186623}=\sqrt{64}*\sqrt{186623}=8\sqrt{186623}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3456)-8\sqrt{186623}}{2*16}=\frac{-3456-8\sqrt{186623}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3456)+8\sqrt{186623}}{2*16}=\frac{-3456+8\sqrt{186623}}{32}
$