6.941=(6.015)(x1)+(7.016)(x2)

Solution for 6.941=(6.015)(x1)+(7.016)(x2) equation:

6.941=(6.015)(x1)+(7.016)(x2)

We move all terms to the left:

6.941-((6.015)(x1)+(7.016)(x2))=0


We calculate terms in parentheses: -((6.015)x1+(7.016)x2), so:

(6.015)x1+(7.016)x2

We multiply parentheses

7.016x^2+6.015x

Back to the equation:

-(7.016x^2+6.015x)


We get rid of parentheses

-7.016x^2-6.015x+6.941=0

a = -7.016; b = -6.015; c = +6.941;
Δ = b2-4ac
Δ = -6.0152-4·(-7.016)·6.941
Δ = 230.972449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6.015)-\sqrt{230.972449}}{2*-7.016}=\frac{6.015-\sqrt{230.972449}}{-14.032}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6.015)+\sqrt{230.972449}}{2*-7.016}=\frac{6.015+\sqrt{230.972449}}{-14.032}
$