7x(3x+5)=-8x+43

Solution for 7x(3x+5)=-8x+43 equation:

7x(3x+5)=-8x+43

We move all terms to the left:

7x(3x+5)-(-8x+43)=0

We multiply parentheses

21x^2+35x-(-8x+43)=0

We get rid of parentheses

21x^2+35x+8x-43=0

We add all the numbers together, and all the variables

21x^2+43x-43=0

a = 21; b = 43; c = -43;
Δ = b2-4ac
Δ = 432-4·21·(-43)
Δ = 5461
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{-(43)-\sqrt{5461}}{2*21}=\frac{-43-\sqrt{5461}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+\sqrt{5461}}{2*21}=\frac{-43+\sqrt{5461}}{42}
$